diff --git a/.github/actions/run-python-test-set/action.yml b/.github/actions/run-python-test-set/action.yml
index 22447025cb..a4bcaff56d 100644
--- a/.github/actions/run-python-test-set/action.yml
+++ b/.github/actions/run-python-test-set/action.yml
@@ -149,7 +149,7 @@ runs:
         fi
 
     - name: Upload Allure results
-      if: ${{ always() && (inputs.test_selection == 'batch_others' || inputs.test_selection == 'batch_pg_regress') }}
+      if: ${{ always() && (inputs.test_selection == 'regress') }}
       uses: ./.github/actions/allure-report
       with:
         action: store
diff --git a/.github/workflows/build_and_test.yml b/.github/workflows/build_and_test.yml
index bf6eb69930..8b1dc3a9c4 100644
--- a/.github/workflows/build_and_test.yml
+++ b/.github/workflows/build_and_test.yml
@@ -206,7 +206,7 @@ jobs:
         if: matrix.build_type == 'debug'
         uses: ./.github/actions/save-coverage-data
 
-  pg_regress-tests:
+  regress-tests:
     runs-on: dev
     container:
       image: 369495373322.dkr.ecr.eu-central-1.amazonaws.com/rust:pinned
@@ -224,42 +224,13 @@ jobs:
           submodules: true
           fetch-depth: 2
 
-      - name: Pytest regress tests
+      - name: Pytest regression tests
         uses: ./.github/actions/run-python-test-set
         with:
           build_type: ${{ matrix.build_type }}
           rust_toolchain: ${{ matrix.rust_toolchain }}
-          test_selection: batch_pg_regress
+          test_selection: regress
           needs_postgres_source: true
-
-      - name: Merge and upload coverage data
-        if: matrix.build_type == 'debug'
-        uses: ./.github/actions/save-coverage-data
-
-  other-tests:
-    runs-on: dev
-    container:
-      image: 369495373322.dkr.ecr.eu-central-1.amazonaws.com/rust:pinned
-      options: --init
-    needs: [ build-neon ]
-    strategy:
-      fail-fast: false
-      matrix:
-        build_type: [ debug, release ]
-        rust_toolchain: [ 1.58 ]
-    steps:
-      - name: Checkout
-        uses: actions/checkout@v3
-        with:
-          submodules: true
-          fetch-depth: 2
-
-      - name: Pytest other tests
-        uses: ./.github/actions/run-python-test-set
-        with:
-          build_type: ${{ matrix.build_type }}
-          rust_toolchain: ${{ matrix.rust_toolchain }}
-          test_selection: batch_others
           run_with_real_s3: true
           real_s3_bucket: ci-tests-s3
           real_s3_region: us-west-2
@@ -307,7 +278,7 @@ jobs:
     container:
       image: 369495373322.dkr.ecr.eu-central-1.amazonaws.com/rust:pinned
       options: --init
-    needs: [ other-tests, pg_regress-tests ]
+    needs: [ regress-tests ]
     if: always()
     strategy:
       fail-fast: false
@@ -330,7 +301,7 @@ jobs:
     container:
       image: 369495373322.dkr.ecr.eu-central-1.amazonaws.com/rust:pinned
       options: --init
-    needs: [ other-tests, pg_regress-tests ]
+    needs: [ regress-tests ]
     strategy:
       fail-fast: false
       matrix:
@@ -587,7 +558,7 @@ jobs:
     #container: 369495373322.dkr.ecr.eu-central-1.amazonaws.com/base:latest
     # We need both storage **and** compute images for deploy, because control plane picks the compute version based on the storage version.
     # If it notices a fresh storage it may bump the compute version. And if compute image failed to build it may break things badly
-    needs: [ push-docker-hub, calculate-deploy-targets, tag, other-tests, pg_regress-tests ]
+    needs: [ push-docker-hub, calculate-deploy-targets, tag, regress-tests ]
     if: |
       (github.ref_name == 'main' || github.ref_name == 'release') &&
       github.event_name != 'workflow_dispatch'
@@ -642,7 +613,7 @@ jobs:
     runs-on: dev
     container: 369495373322.dkr.ecr.eu-central-1.amazonaws.com/base:latest
     # Compute image isn't strictly required for proxy deploy, but let's still wait for it to run all deploy jobs consistently.
-    needs: [ push-docker-hub, calculate-deploy-targets, tag, other-tests, pg_regress-tests ]
+    needs: [ push-docker-hub, calculate-deploy-targets, tag, regress-tests ]
     if: |
       (github.ref_name == 'main' || github.ref_name == 'release') &&
       github.event_name != 'workflow_dispatch'
diff --git a/pageserver/src/page_service.rs b/pageserver/src/page_service.rs
index fbc70f7690..d59a82d488 100644
--- a/pageserver/src/page_service.rs
+++ b/pageserver/src/page_service.rs
@@ -1077,7 +1077,7 @@ impl postgres_backend::Handler for PageServerHandler {
             .write_message(&BeMessage::CommandComplete(b"SELECT 1"))?;
         } else if query_string.starts_with("do_gc ") {
             // Run GC immediately on given timeline.
-            // FIXME: This is just for tests. See test_runner/batch_others/test_gc.py.
+            // FIXME: This is just for tests. See test_runner/regress/test_gc.py.
             // This probably should require special authentication or a global flag to
             // enable, I don't think we want to or need to allow regular clients to invoke
             // GC.
diff --git a/test_runner/README.md b/test_runner/README.md
index 4b54c45175..c7ec361d65 100644
--- a/test_runner/README.md
+++ b/test_runner/README.md
@@ -15,12 +15,22 @@ Prerequisites:
 
 ### Test Organization
 
-The tests are divided into a few batches, such that each batch takes roughly
-the same amount of time. The batches can be run in parallel, to minimize total
-runtime. Currently, there are only two batches:
+Regression tests are in the 'regress' directory. They can be run in
+parallel to minimize total runtime. Most regression test sets up their
+environment with its own pageservers and safekeepers (but see
+`TEST_SHARED_FIXTURES`).
 
-- test_batch_pg_regress: Runs PostgreSQL regression tests
-- test_others: All other tests
+'pg_clients' contains tests for connecting with various client
+libraries. Each client test uses a Dockerfile that pulls an image that
+contains the client, and connects to PostgreSQL with it. The client
+tests can be run against an existing PostgreSQL or Neon installation.
+
+'performance' contains performance regression tests. Each test
+exercises a particular scenario or workload, and outputs
+measurements. They should be run serially, to avoid the tests
+interfering with the performance of each other. Some performance tests
+set up their own Neon environment, while others can be run against an
+existing PostgreSQL or Neon environment.
 
 ### Running the tests
 
diff --git a/test_runner/batch_pg_regress/test_isolation.py b/test_runner/batch_pg_regress/test_isolation.py
deleted file mode 100644
index 7127a069b0..0000000000
--- a/test_runner/batch_pg_regress/test_isolation.py
+++ /dev/null
@@ -1,50 +0,0 @@
-import os
-from pathlib import Path
-
-import pytest
-from fixtures.neon_fixtures import NeonEnv, base_dir, pg_distrib_dir
-
-
-# The isolation tests run for a long time, especially in debug mode,
-# so use a larger-than-default timeout.
-@pytest.mark.timeout(1800)
-def test_isolation(neon_simple_env: NeonEnv, test_output_dir: Path, pg_bin, capsys):
-    env = neon_simple_env
-
-    env.neon_cli.create_branch("test_isolation", "empty")
-    # Connect to postgres and create a database called "regression".
-    # isolation tests use prepared transactions, so enable them
-    pg = env.postgres.create_start("test_isolation", config_lines=["max_prepared_transactions=100"])
-    pg.safe_psql("CREATE DATABASE isolation_regression")
-
-    # Create some local directories for pg_isolation_regress to run in.
-    runpath = test_output_dir / "regress"
-    (runpath / "testtablespace").mkdir(parents=True)
-
-    # Compute all the file locations that pg_isolation_regress will need.
-    build_path = os.path.join(pg_distrib_dir, "build/src/test/isolation")
-    src_path = os.path.join(base_dir, "vendor/postgres/src/test/isolation")
-    bindir = os.path.join(pg_distrib_dir, "bin")
-    schedule = os.path.join(src_path, "isolation_schedule")
-    pg_isolation_regress = os.path.join(build_path, "pg_isolation_regress")
-
-    pg_isolation_regress_command = [
-        pg_isolation_regress,
-        "--use-existing",
-        "--bindir={}".format(bindir),
-        "--dlpath={}".format(build_path),
-        "--inputdir={}".format(src_path),
-        "--schedule={}".format(schedule),
-    ]
-
-    env_vars = {
-        "PGPORT": str(pg.default_options["port"]),
-        "PGUSER": pg.default_options["user"],
-        "PGHOST": pg.default_options["host"],
-    }
-
-    # Run the command.
-    # We don't capture the output. It's not too chatty, and it always
-    # logs the exact same data to `regression.out` anyway.
-    with capsys.disabled():
-        pg_bin.run(pg_isolation_regress_command, env=env_vars, cwd=runpath)
diff --git a/test_runner/batch_pg_regress/test_neon_regress.py b/test_runner/batch_pg_regress/test_neon_regress.py
deleted file mode 100644
index 4619647084..0000000000
--- a/test_runner/batch_pg_regress/test_neon_regress.py
+++ /dev/null
@@ -1,55 +0,0 @@
-import os
-from pathlib import Path
-
-from fixtures.log_helper import log
-from fixtures.neon_fixtures import NeonEnv, base_dir, check_restored_datadir_content, pg_distrib_dir
-
-
-def test_neon_regress(neon_simple_env: NeonEnv, test_output_dir: Path, pg_bin, capsys):
-    env = neon_simple_env
-
-    env.neon_cli.create_branch("test_neon_regress", "empty")
-    # Connect to postgres and create a database called "regression".
-    pg = env.postgres.create_start("test_neon_regress")
-    pg.safe_psql("CREATE DATABASE regression")
-
-    # Create some local directories for pg_regress to run in.
-    runpath = test_output_dir / "regress"
-    (runpath / "testtablespace").mkdir(parents=True)
-
-    # Compute all the file locations that pg_regress will need.
-    # This test runs neon specific tests
-    build_path = os.path.join(pg_distrib_dir, "build/src/test/regress")
-    src_path = os.path.join(base_dir, "test_runner/neon_regress")
-    bindir = os.path.join(pg_distrib_dir, "bin")
-    schedule = os.path.join(src_path, "parallel_schedule")
-    pg_regress = os.path.join(build_path, "pg_regress")
-
-    pg_regress_command = [
-        pg_regress,
-        "--use-existing",
-        "--bindir={}".format(bindir),
-        "--dlpath={}".format(build_path),
-        "--schedule={}".format(schedule),
-        "--inputdir={}".format(src_path),
-    ]
-
-    log.info(pg_regress_command)
-    env_vars = {
-        "PGPORT": str(pg.default_options["port"]),
-        "PGUSER": pg.default_options["user"],
-        "PGHOST": pg.default_options["host"],
-    }
-
-    # Run the command.
-    # We don't capture the output. It's not too chatty, and it always
-    # logs the exact same data to `regression.out` anyway.
-    with capsys.disabled():
-        pg_bin.run(pg_regress_command, env=env_vars, cwd=runpath)
-
-        # checkpoint one more time to ensure that the lsn we get is the latest one
-        pg.safe_psql("CHECKPOINT")
-        pg.safe_psql("select pg_current_wal_insert_lsn()")[0][0]
-
-        # Check that we restore the content of the datadir correctly
-        check_restored_datadir_content(test_output_dir, env, pg)
diff --git a/test_runner/batch_pg_regress/test_pg_regress.py b/test_runner/batch_pg_regress/test_pg_regress.py
deleted file mode 100644
index 478dbf0a91..0000000000
--- a/test_runner/batch_pg_regress/test_pg_regress.py
+++ /dev/null
@@ -1,56 +0,0 @@
-import os
-import pathlib
-
-import pytest
-from fixtures.neon_fixtures import NeonEnv, base_dir, check_restored_datadir_content, pg_distrib_dir
-
-
-# The pg_regress tests run for a long time, especially in debug mode,
-# so use a larger-than-default timeout.
-@pytest.mark.timeout(1800)
-def test_pg_regress(neon_simple_env: NeonEnv, test_output_dir: pathlib.Path, pg_bin, capsys):
-    env = neon_simple_env
-
-    env.neon_cli.create_branch("test_pg_regress", "empty")
-    # Connect to postgres and create a database called "regression".
-    pg = env.postgres.create_start("test_pg_regress")
-    pg.safe_psql("CREATE DATABASE regression")
-
-    # Create some local directories for pg_regress to run in.
-    runpath = test_output_dir / "regress"
-    (runpath / "testtablespace").mkdir(parents=True)
-
-    # Compute all the file locations that pg_regress will need.
-    build_path = os.path.join(pg_distrib_dir, "build/src/test/regress")
-    src_path = os.path.join(base_dir, "vendor/postgres/src/test/regress")
-    bindir = os.path.join(pg_distrib_dir, "bin")
-    schedule = os.path.join(src_path, "parallel_schedule")
-    pg_regress = os.path.join(build_path, "pg_regress")
-
-    pg_regress_command = [
-        pg_regress,
-        '--bindir=""',
-        "--use-existing",
-        "--bindir={}".format(bindir),
-        "--dlpath={}".format(build_path),
-        "--schedule={}".format(schedule),
-        "--inputdir={}".format(src_path),
-    ]
-
-    env_vars = {
-        "PGPORT": str(pg.default_options["port"]),
-        "PGUSER": pg.default_options["user"],
-        "PGHOST": pg.default_options["host"],
-    }
-
-    # Run the command.
-    # We don't capture the output. It's not too chatty, and it always
-    # logs the exact same data to `regression.out` anyway.
-    with capsys.disabled():
-        pg_bin.run(pg_regress_command, env=env_vars, cwd=runpath)
-
-        # checkpoint one more time to ensure that the lsn we get is the latest one
-        pg.safe_psql("CHECKPOINT")
-
-        # Check that we restore the content of the datadir correctly
-        check_restored_datadir_content(test_output_dir, env, pg)
diff --git a/test_runner/neon_regress/README.md b/test_runner/neon_regress/README.md
deleted file mode 100644
index b23a55462e..0000000000
--- a/test_runner/neon_regress/README.md
+++ /dev/null
@@ -1,8 +0,0 @@
-To add a new SQL test
-
-- add sql script to run to neon_regress/sql/testname.sql
-- add expected output to neon_regress/expected/testname.out
-- add testname to parallel_schedule
-
-That's it.
-For more complex tests see PostgreSQL regression tests. These works basically the same.
diff --git a/test_runner/batch_others/test_ancestor_branch.py b/test_runner/regress/test_ancestor_branch.py
similarity index 100%
rename from test_runner/batch_others/test_ancestor_branch.py
rename to test_runner/regress/test_ancestor_branch.py
diff --git a/test_runner/batch_others/test_auth.py b/test_runner/regress/test_auth.py
similarity index 100%
rename from test_runner/batch_others/test_auth.py
rename to test_runner/regress/test_auth.py
diff --git a/test_runner/batch_others/test_backpressure.py b/test_runner/regress/test_backpressure.py
similarity index 100%
rename from test_runner/batch_others/test_backpressure.py
rename to test_runner/regress/test_backpressure.py
diff --git a/test_runner/batch_others/test_basebackup_error.py b/test_runner/regress/test_basebackup_error.py
similarity index 100%
rename from test_runner/batch_others/test_basebackup_error.py
rename to test_runner/regress/test_basebackup_error.py
diff --git a/test_runner/batch_others/test_branch_and_gc.py b/test_runner/regress/test_branch_and_gc.py
similarity index 100%
rename from test_runner/batch_others/test_branch_and_gc.py
rename to test_runner/regress/test_branch_and_gc.py
diff --git a/test_runner/batch_others/test_branch_behind.py b/test_runner/regress/test_branch_behind.py
similarity index 100%
rename from test_runner/batch_others/test_branch_behind.py
rename to test_runner/regress/test_branch_behind.py
diff --git a/test_runner/batch_others/test_branching.py b/test_runner/regress/test_branching.py
similarity index 91%
rename from test_runner/batch_others/test_branching.py
rename to test_runner/regress/test_branching.py
index 2d08b07f82..0c1490294d 100644
--- a/test_runner/batch_others/test_branching.py
+++ b/test_runner/regress/test_branching.py
@@ -62,10 +62,11 @@ def test_branching_with_pgbench(
         time.sleep(delay)
         log.info(f"Sleep {delay}s")
 
-        # If the number of concurrent threads exceeds a threshold,
-        # wait for all the threads to finish before spawning a new one.
-        # Because tests defined in `batch_others` are run concurrently in CI,
-        # we want to avoid the situation that one test exhausts resources for other tests.
+        # If the number of concurrent threads exceeds a threshold, wait for
+        # all the threads to finish before spawning a new one. Because the
+        # regression tests in this directory are run concurrently in CI, we
+        # want to avoid the situation that one test exhausts resources for
+        # other tests.
         if len(threads) >= thread_limit:
             for thread in threads:
                 thread.join()
diff --git a/test_runner/batch_others/test_broken_timeline.py b/test_runner/regress/test_broken_timeline.py
similarity index 100%
rename from test_runner/batch_others/test_broken_timeline.py
rename to test_runner/regress/test_broken_timeline.py
diff --git a/test_runner/batch_others/test_clog_truncate.py b/test_runner/regress/test_clog_truncate.py
similarity index 100%
rename from test_runner/batch_others/test_clog_truncate.py
rename to test_runner/regress/test_clog_truncate.py
diff --git a/test_runner/batch_others/test_close_fds.py b/test_runner/regress/test_close_fds.py
similarity index 100%
rename from test_runner/batch_others/test_close_fds.py
rename to test_runner/regress/test_close_fds.py
diff --git a/test_runner/batch_others/test_config.py b/test_runner/regress/test_config.py
similarity index 100%
rename from test_runner/batch_others/test_config.py
rename to test_runner/regress/test_config.py
diff --git a/test_runner/batch_others/test_crafted_wal_end.py b/test_runner/regress/test_crafted_wal_end.py
similarity index 100%
rename from test_runner/batch_others/test_crafted_wal_end.py
rename to test_runner/regress/test_crafted_wal_end.py
diff --git a/test_runner/batch_others/test_createdropdb.py b/test_runner/regress/test_createdropdb.py
similarity index 100%
rename from test_runner/batch_others/test_createdropdb.py
rename to test_runner/regress/test_createdropdb.py
diff --git a/test_runner/batch_others/test_createuser.py b/test_runner/regress/test_createuser.py
similarity index 100%
rename from test_runner/batch_others/test_createuser.py
rename to test_runner/regress/test_createuser.py
diff --git a/test_runner/batch_others/test_fsm_truncate.py b/test_runner/regress/test_fsm_truncate.py
similarity index 100%
rename from test_runner/batch_others/test_fsm_truncate.py
rename to test_runner/regress/test_fsm_truncate.py
diff --git a/test_runner/batch_others/test_fullbackup.py b/test_runner/regress/test_fullbackup.py
similarity index 100%
rename from test_runner/batch_others/test_fullbackup.py
rename to test_runner/regress/test_fullbackup.py
diff --git a/test_runner/batch_others/test_gc_aggressive.py b/test_runner/regress/test_gc_aggressive.py
similarity index 100%
rename from test_runner/batch_others/test_gc_aggressive.py
rename to test_runner/regress/test_gc_aggressive.py
diff --git a/test_runner/batch_others/test_import.py b/test_runner/regress/test_import.py
similarity index 100%
rename from test_runner/batch_others/test_import.py
rename to test_runner/regress/test_import.py
diff --git a/test_runner/batch_others/test_large_schema.py b/test_runner/regress/test_large_schema.py
similarity index 100%
rename from test_runner/batch_others/test_large_schema.py
rename to test_runner/regress/test_large_schema.py
diff --git a/test_runner/batch_others/test_lsn_mapping.py b/test_runner/regress/test_lsn_mapping.py
similarity index 100%
rename from test_runner/batch_others/test_lsn_mapping.py
rename to test_runner/regress/test_lsn_mapping.py
diff --git a/test_runner/batch_others/test_multixact.py b/test_runner/regress/test_multixact.py
similarity index 100%
rename from test_runner/batch_others/test_multixact.py
rename to test_runner/regress/test_multixact.py
diff --git a/test_runner/batch_others/test_neon_cli.py b/test_runner/regress/test_neon_cli.py
similarity index 100%
rename from test_runner/batch_others/test_neon_cli.py
rename to test_runner/regress/test_neon_cli.py
diff --git a/test_runner/batch_others/test_next_xid.py b/test_runner/regress/test_next_xid.py
similarity index 100%
rename from test_runner/batch_others/test_next_xid.py
rename to test_runner/regress/test_next_xid.py
diff --git a/test_runner/batch_others/test_normal_work.py b/test_runner/regress/test_normal_work.py
similarity index 100%
rename from test_runner/batch_others/test_normal_work.py
rename to test_runner/regress/test_normal_work.py
diff --git a/test_runner/batch_others/test_old_request_lsn.py b/test_runner/regress/test_old_request_lsn.py
similarity index 100%
rename from test_runner/batch_others/test_old_request_lsn.py
rename to test_runner/regress/test_old_request_lsn.py
diff --git a/test_runner/batch_others/test_pageserver_api.py b/test_runner/regress/test_pageserver_api.py
similarity index 100%
rename from test_runner/batch_others/test_pageserver_api.py
rename to test_runner/regress/test_pageserver_api.py
diff --git a/test_runner/batch_others/test_pageserver_catchup.py b/test_runner/regress/test_pageserver_catchup.py
similarity index 100%
rename from test_runner/batch_others/test_pageserver_catchup.py
rename to test_runner/regress/test_pageserver_catchup.py
diff --git a/test_runner/batch_others/test_pageserver_restart.py b/test_runner/regress/test_pageserver_restart.py
similarity index 100%
rename from test_runner/batch_others/test_pageserver_restart.py
rename to test_runner/regress/test_pageserver_restart.py
diff --git a/test_runner/batch_others/test_parallel_copy.py b/test_runner/regress/test_parallel_copy.py
similarity index 100%
rename from test_runner/batch_others/test_parallel_copy.py
rename to test_runner/regress/test_parallel_copy.py
diff --git a/test_runner/regress/test_pg_regress.py b/test_runner/regress/test_pg_regress.py
new file mode 100644
index 0000000000..119528b8f9
--- /dev/null
+++ b/test_runner/regress/test_pg_regress.py
@@ -0,0 +1,159 @@
+#
+# This file runs pg_regress-based tests.
+#
+import os
+from pathlib import Path
+
+import pytest
+from fixtures.neon_fixtures import NeonEnv, base_dir, check_restored_datadir_content, pg_distrib_dir
+
+
+# Run the main PostgreSQL regression tests, in src/test/regress.
+#
+# This runs for a long time, especially in debug mode, so use a larger-than-default
+# timeout.
+@pytest.mark.timeout(1800)
+def test_pg_regress(neon_simple_env: NeonEnv, test_output_dir: Path, pg_bin, capsys):
+    env = neon_simple_env
+
+    env.neon_cli.create_branch("test_pg_regress", "empty")
+    # Connect to postgres and create a database called "regression".
+    pg = env.postgres.create_start("test_pg_regress")
+    pg.safe_psql("CREATE DATABASE regression")
+
+    # Create some local directories for pg_regress to run in.
+    runpath = test_output_dir / "regress"
+    (runpath / "testtablespace").mkdir(parents=True)
+
+    # Compute all the file locations that pg_regress will need.
+    build_path = os.path.join(pg_distrib_dir, "build/src/test/regress")
+    src_path = os.path.join(base_dir, "vendor/postgres/src/test/regress")
+    bindir = os.path.join(pg_distrib_dir, "bin")
+    schedule = os.path.join(src_path, "parallel_schedule")
+    pg_regress = os.path.join(build_path, "pg_regress")
+
+    pg_regress_command = [
+        pg_regress,
+        '--bindir=""',
+        "--use-existing",
+        "--bindir={}".format(bindir),
+        "--dlpath={}".format(build_path),
+        "--schedule={}".format(schedule),
+        "--inputdir={}".format(src_path),
+    ]
+
+    env_vars = {
+        "PGPORT": str(pg.default_options["port"]),
+        "PGUSER": pg.default_options["user"],
+        "PGHOST": pg.default_options["host"],
+    }
+
+    # Run the command.
+    # We don't capture the output. It's not too chatty, and it always
+    # logs the exact same data to `regression.out` anyway.
+    with capsys.disabled():
+        pg_bin.run(pg_regress_command, env=env_vars, cwd=runpath)
+
+        # checkpoint one more time to ensure that the lsn we get is the latest one
+        pg.safe_psql("CHECKPOINT")
+
+        # Check that we restore the content of the datadir correctly
+        check_restored_datadir_content(test_output_dir, env, pg)
+
+
+# Run the PostgreSQL "isolation" tests, in src/test/isolation.
+#
+# This runs for a long time, especially in debug mode, so use a larger-than-default
+# timeout.
+@pytest.mark.timeout(1800)
+def test_isolation(neon_simple_env: NeonEnv, test_output_dir: Path, pg_bin, capsys):
+    env = neon_simple_env
+
+    env.neon_cli.create_branch("test_isolation", "empty")
+    # Connect to postgres and create a database called "regression".
+    # isolation tests use prepared transactions, so enable them
+    pg = env.postgres.create_start("test_isolation", config_lines=["max_prepared_transactions=100"])
+    pg.safe_psql("CREATE DATABASE isolation_regression")
+
+    # Create some local directories for pg_isolation_regress to run in.
+    runpath = test_output_dir / "regress"
+    (runpath / "testtablespace").mkdir(parents=True)
+
+    # Compute all the file locations that pg_isolation_regress will need.
+    build_path = os.path.join(pg_distrib_dir, "build/src/test/isolation")
+    src_path = os.path.join(base_dir, "vendor/postgres/src/test/isolation")
+    bindir = os.path.join(pg_distrib_dir, "bin")
+    schedule = os.path.join(src_path, "isolation_schedule")
+    pg_isolation_regress = os.path.join(build_path, "pg_isolation_regress")
+
+    pg_isolation_regress_command = [
+        pg_isolation_regress,
+        "--use-existing",
+        "--bindir={}".format(bindir),
+        "--dlpath={}".format(build_path),
+        "--inputdir={}".format(src_path),
+        "--schedule={}".format(schedule),
+    ]
+
+    env_vars = {
+        "PGPORT": str(pg.default_options["port"]),
+        "PGUSER": pg.default_options["user"],
+        "PGHOST": pg.default_options["host"],
+    }
+
+    # Run the command.
+    # We don't capture the output. It's not too chatty, and it always
+    # logs the exact same data to `regression.out` anyway.
+    with capsys.disabled():
+        pg_bin.run(pg_isolation_regress_command, env=env_vars, cwd=runpath)
+
+
+# Run extra Neon-specific pg_regress-based tests. The tests and their
+# schedule file are in the sql_regress/ directory.
+def test_sql_regress(neon_simple_env: NeonEnv, test_output_dir: Path, pg_bin, capsys):
+    env = neon_simple_env
+
+    env.neon_cli.create_branch("test_sql_regress", "empty")
+    # Connect to postgres and create a database called "regression".
+    pg = env.postgres.create_start("test_sql_regress")
+    pg.safe_psql("CREATE DATABASE regression")
+
+    # Create some local directories for pg_regress to run in.
+    runpath = test_output_dir / "regress"
+    (runpath / "testtablespace").mkdir(parents=True)
+
+    # Compute all the file locations that pg_regress will need.
+    # This test runs neon specific tests
+    build_path = os.path.join(pg_distrib_dir, "build/src/test/regress")
+    src_path = os.path.join(base_dir, "test_runner/sql_regress")
+    bindir = os.path.join(pg_distrib_dir, "bin")
+    schedule = os.path.join(src_path, "parallel_schedule")
+    pg_regress = os.path.join(build_path, "pg_regress")
+
+    pg_regress_command = [
+        pg_regress,
+        "--use-existing",
+        "--bindir={}".format(bindir),
+        "--dlpath={}".format(build_path),
+        "--schedule={}".format(schedule),
+        "--inputdir={}".format(src_path),
+    ]
+
+    env_vars = {
+        "PGPORT": str(pg.default_options["port"]),
+        "PGUSER": pg.default_options["user"],
+        "PGHOST": pg.default_options["host"],
+    }
+
+    # Run the command.
+    # We don't capture the output. It's not too chatty, and it always
+    # logs the exact same data to `regression.out` anyway.
+    with capsys.disabled():
+        pg_bin.run(pg_regress_command, env=env_vars, cwd=runpath)
+
+        # checkpoint one more time to ensure that the lsn we get is the latest one
+        pg.safe_psql("CHECKPOINT")
+        pg.safe_psql("select pg_current_wal_insert_lsn()")[0][0]
+
+        # Check that we restore the content of the datadir correctly
+        check_restored_datadir_content(test_output_dir, env, pg)
diff --git a/test_runner/batch_others/test_pitr_gc.py b/test_runner/regress/test_pitr_gc.py
similarity index 100%
rename from test_runner/batch_others/test_pitr_gc.py
rename to test_runner/regress/test_pitr_gc.py
diff --git a/test_runner/batch_others/test_proxy.py b/test_runner/regress/test_proxy.py
similarity index 100%
rename from test_runner/batch_others/test_proxy.py
rename to test_runner/regress/test_proxy.py
diff --git a/test_runner/batch_others/test_read_validation.py b/test_runner/regress/test_read_validation.py
similarity index 100%
rename from test_runner/batch_others/test_read_validation.py
rename to test_runner/regress/test_read_validation.py
diff --git a/test_runner/batch_others/test_readonly_node.py b/test_runner/regress/test_readonly_node.py
similarity index 100%
rename from test_runner/batch_others/test_readonly_node.py
rename to test_runner/regress/test_readonly_node.py
diff --git a/test_runner/batch_others/test_recovery.py b/test_runner/regress/test_recovery.py
similarity index 100%
rename from test_runner/batch_others/test_recovery.py
rename to test_runner/regress/test_recovery.py
diff --git a/test_runner/batch_others/test_remote_storage.py b/test_runner/regress/test_remote_storage.py
similarity index 100%
rename from test_runner/batch_others/test_remote_storage.py
rename to test_runner/regress/test_remote_storage.py
diff --git a/test_runner/batch_others/test_setup.py b/test_runner/regress/test_setup.py
similarity index 100%
rename from test_runner/batch_others/test_setup.py
rename to test_runner/regress/test_setup.py
diff --git a/test_runner/batch_others/test_subxacts.py b/test_runner/regress/test_subxacts.py
similarity index 100%
rename from test_runner/batch_others/test_subxacts.py
rename to test_runner/regress/test_subxacts.py
diff --git a/test_runner/batch_others/test_tenant_conf.py b/test_runner/regress/test_tenant_conf.py
similarity index 100%
rename from test_runner/batch_others/test_tenant_conf.py
rename to test_runner/regress/test_tenant_conf.py
diff --git a/test_runner/batch_others/test_tenant_detach.py b/test_runner/regress/test_tenant_detach.py
similarity index 100%
rename from test_runner/batch_others/test_tenant_detach.py
rename to test_runner/regress/test_tenant_detach.py
diff --git a/test_runner/batch_others/test_tenant_relocation.py b/test_runner/regress/test_tenant_relocation.py
similarity index 100%
rename from test_runner/batch_others/test_tenant_relocation.py
rename to test_runner/regress/test_tenant_relocation.py
diff --git a/test_runner/batch_others/test_tenant_tasks.py b/test_runner/regress/test_tenant_tasks.py
similarity index 100%
rename from test_runner/batch_others/test_tenant_tasks.py
rename to test_runner/regress/test_tenant_tasks.py
diff --git a/test_runner/batch_others/test_tenants.py b/test_runner/regress/test_tenants.py
similarity index 100%
rename from test_runner/batch_others/test_tenants.py
rename to test_runner/regress/test_tenants.py
diff --git a/test_runner/batch_others/test_tenants_with_remote_storage.py b/test_runner/regress/test_tenants_with_remote_storage.py
similarity index 100%
rename from test_runner/batch_others/test_tenants_with_remote_storage.py
rename to test_runner/regress/test_tenants_with_remote_storage.py
diff --git a/test_runner/batch_others/test_timeline_delete.py b/test_runner/regress/test_timeline_delete.py
similarity index 100%
rename from test_runner/batch_others/test_timeline_delete.py
rename to test_runner/regress/test_timeline_delete.py
diff --git a/test_runner/batch_others/test_timeline_size.py b/test_runner/regress/test_timeline_size.py
similarity index 100%
rename from test_runner/batch_others/test_timeline_size.py
rename to test_runner/regress/test_timeline_size.py
diff --git a/test_runner/batch_others/test_twophase.py b/test_runner/regress/test_twophase.py
similarity index 100%
rename from test_runner/batch_others/test_twophase.py
rename to test_runner/regress/test_twophase.py
diff --git a/test_runner/batch_others/test_vm_bits.py b/test_runner/regress/test_vm_bits.py
similarity index 100%
rename from test_runner/batch_others/test_vm_bits.py
rename to test_runner/regress/test_vm_bits.py
diff --git a/test_runner/batch_others/test_wal_acceptor.py b/test_runner/regress/test_wal_acceptor.py
similarity index 100%
rename from test_runner/batch_others/test_wal_acceptor.py
rename to test_runner/regress/test_wal_acceptor.py
diff --git a/test_runner/batch_others/test_wal_acceptor_async.py b/test_runner/regress/test_wal_acceptor_async.py
similarity index 100%
rename from test_runner/batch_others/test_wal_acceptor_async.py
rename to test_runner/regress/test_wal_acceptor_async.py
diff --git a/test_runner/batch_others/test_wal_restore.py b/test_runner/regress/test_wal_restore.py
similarity index 100%
rename from test_runner/batch_others/test_wal_restore.py
rename to test_runner/regress/test_wal_restore.py
diff --git a/test_runner/neon_regress/.gitignore b/test_runner/sql_regress/.gitignore
similarity index 100%
rename from test_runner/neon_regress/.gitignore
rename to test_runner/sql_regress/.gitignore
diff --git a/test_runner/sql_regress/README.md b/test_runner/sql_regress/README.md
new file mode 100644
index 0000000000..1ae8aaf61a
--- /dev/null
+++ b/test_runner/sql_regress/README.md
@@ -0,0 +1,13 @@
+Simple tests that only need a PostgreSQL connection to run.
+These are run by the regress/test_pg_regress.py test, which uses
+the PostgreSQL pg_regress utility.
+
+To add a new SQL test:
+
+- add sql script to run to neon_regress/sql/testname.sql
+- add expected output to neon_regress/expected/testname.out
+- add testname to parallel_schedule
+
+That's it.
+For more complex tests see PostgreSQL regression tests in src/test/regress.
+These work basically the same.
diff --git a/test_runner/neon_regress/expected/.gitignore b/test_runner/sql_regress/expected/.gitignore
similarity index 100%
rename from test_runner/neon_regress/expected/.gitignore
rename to test_runner/sql_regress/expected/.gitignore
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diff --git a/test_runner/neon_regress/expected/neon-vacuum-full.out b/test_runner/sql_regress/expected/neon-vacuum-full.out
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rename from test_runner/neon_regress/expected/neon-vacuum-full.out
rename to test_runner/sql_regress/expected/neon-vacuum-full.out
diff --git a/test_runner/neon_regress/parallel_schedule b/test_runner/sql_regress/parallel_schedule
similarity index 100%
rename from test_runner/neon_regress/parallel_schedule
rename to test_runner/sql_regress/parallel_schedule
diff --git a/test_runner/neon_regress/sql/.gitignore b/test_runner/sql_regress/sql/.gitignore
similarity index 100%
rename from test_runner/neon_regress/sql/.gitignore
rename to test_runner/sql_regress/sql/.gitignore
diff --git a/test_runner/neon_regress/sql/neon-cid.sql b/test_runner/sql_regress/sql/neon-cid.sql
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rename from test_runner/neon_regress/sql/neon-cid.sql
rename to test_runner/sql_regress/sql/neon-cid.sql
diff --git a/test_runner/neon_regress/sql/neon-clog.sql b/test_runner/sql_regress/sql/neon-clog.sql
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rename from test_runner/neon_regress/sql/neon-clog.sql
rename to test_runner/sql_regress/sql/neon-clog.sql
diff --git a/test_runner/neon_regress/sql/neon-rel-truncate.sql b/test_runner/sql_regress/sql/neon-rel-truncate.sql
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rename from test_runner/neon_regress/sql/neon-rel-truncate.sql
rename to test_runner/sql_regress/sql/neon-rel-truncate.sql
diff --git a/test_runner/neon_regress/sql/neon-vacuum-full.sql b/test_runner/sql_regress/sql/neon-vacuum-full.sql
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rename from test_runner/neon_regress/sql/neon-vacuum-full.sql
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