diff --git a/test_runner/batch_others/test_tenant_relocation.py b/test_runner/batch_others/test_tenant_relocation.py
index 80f92b6dae..1eb4fe1a29 100644
--- a/test_runner/batch_others/test_tenant_relocation.py
+++ b/test_runner/batch_others/test_tenant_relocation.py
@@ -12,6 +12,10 @@ import pytest
 from fixtures.zenith_fixtures import PgProtocol, PortDistributor, Postgres, ZenithEnvBuilder, ZenithPageserverHttpClient, zenith_binpath, pg_distrib_dir
 
 
+def assert_abs_margin_ratio(a: float, b: float, margin_ratio: float):
+    assert abs(a - b) / a < margin_ratio, (a, b, margin_ratio)
+
+
 @contextmanager
 def new_pageserver_helper(new_pageserver_dir: pathlib.Path,
                           pageserver_bin: pathlib.Path,
@@ -95,7 +99,9 @@ def load(pg: Postgres, stop_event: threading.Event, load_ok_event: threading.Eve
                     # if we recovered after failure verify that we have correct number of rows
                     log.info("recovering at %s", inserted_ctr)
                     cur.execute("SELECT count(*) FROM load")
-                    assert cur.fetchone()[0] == inserted_ctr
+                    # it seems that sometimes transaction gets commited before we can acknowledge
+                    # the result, so sometimes selected value is larger by one than we expect
+                    assert cur.fetchone()[0] - inserted_ctr <= 1
                     log.info("successfully recovered %s", inserted_ctr)
                     failed = False
                     load_ok_event.set()
@@ -197,22 +203,24 @@ def test_tenant_relocation(zenith_env_builder: ZenithEnvBuilder,
             func=lambda: assert_local(new_pageserver_http_client, tenant, timeline))
         assert new_timeline_detail['timeline_state'].get('Ready'), new_timeline_detail
         # when load is active these checks can break because lsns are not static
+        # so lets check with some margin
         if with_load == 'without_load':
-            assert new_timeline_detail['disk_consistent_lsn'] == timeline_detail[
-                'disk_consistent_lsn']
-            assert new_timeline_detail['timeline_state']['Ready'] == timeline_detail[
-                'timeline_state']['Ready']
+            # TODO revisit this once https://github.com/zenithdb/zenith/issues/1049 is fixed
+            assert_abs_margin_ratio(new_timeline_detail['disk_consistent_lsn'],
+                                    timeline_detail['disk_consistent_lsn'],
+                                    0.01)
+            assert_abs_margin_ratio(new_timeline_detail['timeline_state']['Ready'],
+                                    timeline_detail['timeline_state']['Ready'],
+                                    0.01)
 
         # callmemaybe to start replication from safekeeper to the new pageserver
         # when there is no load there is a clean checkpoint and no wal delta
         # needs to be streamed to the new pageserver
         # TODO (rodionov) use attach to start replication
-        with closing(PgProtocol(host='localhost',
-                                port=new_pageserver_pg_port).connect()) as new_pageserver_pg:
-            with new_pageserver_pg.cursor() as cur:
-                # "callmemaybe {} {} host={} port={} options='-c ztimelineid={} ztenantid={}'"
-                safekeeper_connstring = f"host=localhost port={env.safekeepers[0].port.pg} options='-c ztimelineid={timeline} ztenantid={tenant} pageserver_connstr=postgresql://no_user:@localhost:{new_pageserver_pg_port}'"
-                cur.execute("callmemaybe {} {} {}".format(tenant, timeline, safekeeper_connstring))
+        with pg_cur(PgProtocol(host='localhost', port=new_pageserver_pg_port)) as cur:
+            # "callmemaybe {} {} host={} port={} options='-c ztimelineid={} ztenantid={}'"
+            safekeeper_connstring = f"host=localhost port={env.safekeepers[0].port.pg} options='-c ztimelineid={timeline} ztenantid={tenant} pageserver_connstr=postgresql://no_user:@localhost:{new_pageserver_pg_port}'"
+            cur.execute("callmemaybe {} {} {}".format(tenant, timeline, safekeeper_connstring))
 
         tenant_pg.stop()
 
@@ -234,18 +242,17 @@ def test_tenant_relocation(zenith_env_builder: ZenithEnvBuilder,
         # is no longer involved, and if it is, we will see the errors
         pageserver_http_client.timeline_detach(UUID(tenant), UUID(timeline))
 
-        with closing(tenant_pg.connect()) as conn:
-            with conn.cursor() as cur:
-                # check that data is still there
-                cur.execute("SELECT sum(key) FROM t")
-                assert cur.fetchone() == (500500, )
-                # check that we can write new data
-                cur.execute("INSERT INTO t SELECT generate_series(1001,2000), 'some payload'")
-                cur.execute("SELECT sum(key) FROM t")
-                assert cur.fetchone() == (2001000, )
+        with pg_cur(tenant_pg) as cur:
+            # check that data is still there
+            cur.execute("SELECT sum(key) FROM t")
+            assert cur.fetchone() == (500500, )
+            # check that we can write new data
+            cur.execute("INSERT INTO t SELECT generate_series(1001,2000), 'some payload'")
+            cur.execute("SELECT sum(key) FROM t")
+            assert cur.fetchone() == (2001000, )
 
         if with_load == 'with_load':
-            assert load_ok_event.is_set()
+            assert load_ok_event.wait(1)
             log.info('stopping load thread')
             load_stop_event.set()
             load_thread.join()