diff --git a/pageserver/src/import_datadir.rs b/pageserver/src/import_datadir.rs
index 343dec2ca1..ed409d3130 100644
--- a/pageserver/src/import_datadir.rs
+++ b/pageserver/src/import_datadir.rs
@@ -8,6 +8,7 @@ use anyhow::{bail, ensure, Context, Result};
 use bytes::Bytes;
 use camino::Utf8Path;
 use futures::StreamExt;
+use pageserver_api::key::rel_block_to_key;
 use tokio::io::{AsyncRead, AsyncReadExt};
 use tokio_tar::Archive;
 use tracing::*;
@@ -170,7 +171,10 @@ async fn import_rel(
         let r = reader.read_exact(&mut buf).await;
         match r {
             Ok(_) => {
-                modification.put_rel_page_image(rel, blknum, Bytes::copy_from_slice(&buf))?;
+                let key = rel_block_to_key(rel, blknum);
+                if modification.tline.get_shard_identity().is_key_local(&key) {
+                    modification.put_rel_page_image(rel, blknum, Bytes::copy_from_slice(&buf))?;
+                }
             }
 
             // TODO: UnexpectedEof is expected
diff --git a/test_runner/fixtures/workload.py b/test_runner/fixtures/workload.py
index 4ebc02e6fd..364b8a1cf0 100644
--- a/test_runner/fixtures/workload.py
+++ b/test_runner/fixtures/workload.py
@@ -81,9 +81,13 @@ class Workload:
 
         return self._endpoint
 
-    def __del__(self):
+    def stop(self):
         if self._endpoint is not None:
             self._endpoint.stop()
+            self._endpoint = None
+
+    def __del__(self):
+        self.stop()
 
     def stop(self):
         if self._endpoint is not None:
diff --git a/test_runner/regress/test_sharding.py b/test_runner/regress/test_sharding.py
index bca11bbbe7..bfaab9125f 100644
--- a/test_runner/regress/test_sharding.py
+++ b/test_runner/regress/test_sharding.py
@@ -10,11 +10,13 @@ from fixtures.log_helper import log
 from fixtures.neon_fixtures import (
     NeonEnv,
     NeonEnvBuilder,
+    S3Scrubber,
     StorageControllerApiException,
     last_flush_lsn_upload,
     tenant_get_shards,
     wait_for_last_flush_lsn,
 )
+from fixtures.pageserver.utils import assert_prefix_empty, assert_prefix_not_empty
 from fixtures.remote_storage import s3_storage
 from fixtures.types import Lsn, TenantId, TenantShardId, TimelineId
 from fixtures.utils import wait_until
@@ -69,6 +71,15 @@ def test_sharding_smoke(
         log.info(f"sizes = {sizes}")
         return sizes
 
+    # The imported initdb for timeline creation should
+    # not be fully imported on every shard.  We use a 1MB strripe size so expect
+    # pretty good distribution: no one shard should have more than half the data
+    sizes = get_sizes()
+    physical_initdb_total = sum(sizes.values())
+    expect_initdb_size = 20 * 1024 * 1024
+    assert physical_initdb_total > expect_initdb_size
+    assert all(s < expect_initdb_size // 2 for s in sizes.values())
+
     # Test that timeline creation works on a sharded tenant
     timeline_b = env.neon_cli.create_branch("branch_b", tenant_id=tenant_id)
 
@@ -101,6 +112,38 @@ def test_sharding_smoke(
 
     env.storage_controller.consistency_check()
 
+    # Validate that deleting a sharded tenant removes all files in the prefix
+
+    # Before deleting, stop the client and check we have some objects to delete
+    workload.stop()
+    assert_prefix_not_empty(
+        neon_env_builder.pageserver_remote_storage,
+        prefix="/".join(
+            (
+                "tenants",
+                str(tenant_id),
+            )
+        ),
+    )
+
+    # Check the scrubber isn't confused by sharded content, then disable
+    # it during teardown because we'll have deleted by then
+    S3Scrubber(neon_env_builder).scan_metadata()
+    neon_env_builder.scrub_on_exit = False
+
+    env.storage_controller.pageserver_api().tenant_delete(tenant_id)
+    assert_prefix_empty(
+        neon_env_builder.pageserver_remote_storage,
+        prefix="/".join(
+            (
+                "tenants",
+                str(tenant_id),
+            )
+        ),
+    )
+
+    env.storage_controller.consistency_check()
+
 
 def test_sharding_split_unsharded(
     neon_env_builder: NeonEnvBuilder,