diff --git a/tests/integration/ha_tests/helpers.py b/tests/integration/ha_tests/helpers.py
index 13a6a38d8..bc7b48e1e 100644
--- a/tests/integration/ha_tests/helpers.py
+++ b/tests/integration/ha_tests/helpers.py
@@ -443,7 +443,7 @@ async def reused_storage(ops_test: OpsTest, unit_name, removal_time) -> bool:
         If member transitions to STARTUP2 from REMOVED then it is re-using the storage we
         provided.
     """
-    cat_cmd = f"run --unit {unit_name} -- cat {MONGODB_LOG_PATH}"
+    cat_cmd = f"exec --unit {unit_name} -- cat {MONGODB_LOG_PATH}"
     return_code, output, _ = await ops_test.juju(*cat_cmd.split())
 
     if return_code != 0:
@@ -521,7 +521,7 @@ async def db_step_down(ops_test: OpsTest, old_primary_unit: str, sigterm_time: i
     app = await app_name(ops_test)
     for unit in ops_test.model.applications[app].units:
         # verify log file exists on this machine
-        search_file = f"run --unit {unit.name} ls {MONGODB_LOG_PATH}"
+        search_file = f"exec --unit {unit.name} ls {MONGODB_LOG_PATH}"
         return_code, _, _ = await ops_test.juju(*search_file.split())
         if return_code == 2:
             continue
@@ -559,7 +559,7 @@ async def all_db_processes_down(ops_test: OpsTest) -> bool:
         for attempt in Retrying(stop=stop_after_attempt(60), wait=wait_fixed(3)):
             with attempt:
                 for unit in ops_test.model.applications[app].units:
-                    search_db_process = f"run --unit {unit.name} pgrep -x mongod"
+                    search_db_process = f"exec --unit {unit.name} pgrep -x mongod"
                     _, processes, _ = await ops_test.juju(*search_db_process.split())
                     # splitting processes by "\n" results in one or more empty lines, hence we
                     # need to process these lines accordingly.
@@ -593,7 +593,7 @@ async def update_restart_delay(ops_test: OpsTest, unit, delay: int):
     # MONGOD_SERVICE_DEFAULT_PATH since this directory has strict permissions, instead we scp it
     # elsewhere and then move it to MONGOD_SERVICE_DEFAULT_PATH.
     await unit.scp_to(source=TMP_SERVICE_PATH, destination="mongod.service")
-    mv_cmd = f"run --unit {unit.name} mv /home/ubuntu/mongod.service {MONGOD_SERVICE_DEFAULT_PATH}"
+    mv_cmd = f"exec --unit {unit.name} mv /home/ubuntu/mongod.service {MONGOD_SERVICE_DEFAULT_PATH}"
     return_code, _, _ = await ops_test.juju(*mv_cmd.split())
     if return_code != 0:
         raise ProcessError(f"Command: {mv_cmd} failed on unit: {unit.name}.")
@@ -602,7 +602,7 @@ async def update_restart_delay(ops_test: OpsTest, unit, delay: int):
     subprocess.call(["rm", TMP_SERVICE_PATH])
 
     # reload the daemon for systemd otherwise changes are not saved
-    reload_cmd = f"run --unit {unit.name} systemctl daemon-reload"
+    reload_cmd = f"exec --unit {unit.name} systemctl daemon-reload"
     return_code, _, _ = await ops_test.juju(*reload_cmd.split())
     if return_code != 0:
         raise ProcessError(f"Command: {reload_cmd} failed on unit: {unit.name}.")
@@ -634,7 +634,7 @@ async def update_service_logging(ops_test: OpsTest, unit, logging: bool):
     # MONGOD_SERVICE_DEFAULT_PATH since this directory has strict permissions, instead we scp it
     # elsewhere and then move it to MONGOD_SERVICE_DEFAULT_PATH.
     await unit.scp_to(source=TMP_SERVICE_PATH, destination="mongod.service")
-    mv_cmd = f"run --unit {unit.name} mv /home/ubuntu/mongod.service {MONGOD_SERVICE_DEFAULT_PATH}"
+    mv_cmd = f"exec --unit {unit.name} mv /home/ubuntu/mongod.service {MONGOD_SERVICE_DEFAULT_PATH}"
     return_code, _, _ = await ops_test.juju(*mv_cmd.split())
     if return_code != 0:
         raise ProcessError(f"Command: {mv_cmd} failed on unit: {unit.name}.")
@@ -643,7 +643,7 @@ async def update_service_logging(ops_test: OpsTest, unit, logging: bool):
     subprocess.call(["rm", TMP_SERVICE_PATH])
 
     # reload the daemon for systemd otherwise changes are not saved
-    reload_cmd = f"run --unit {unit.name} systemctl daemon-reload"
+    reload_cmd = f"exec --unit {unit.name} systemctl daemon-reload"
     return_code, _, _ = await ops_test.juju(*reload_cmd.split())
     if return_code != 0:
         raise ProcessError(f"Command: {reload_cmd} failed on unit: {unit.name}.")
@@ -651,13 +651,13 @@ async def update_service_logging(ops_test: OpsTest, unit, logging: bool):
 
 async def stop_mongod(ops_test: OpsTest, unit) -> None:
     """Safely stops the mongod process."""
-    stop_db_process = f"run --unit {unit.name} snap stop charmed-mongodb.mongod"
+    stop_db_process = f"exec --unit {unit.name} snap stop charmed-mongodb.mongod"
     await ops_test.juju(*stop_db_process.split())
 
 
 async def start_mongod(ops_test: OpsTest, unit) -> None:
     """Safely starts the mongod process."""
-    start_db_process = f"run --unit {unit.name} snap start charmed-mongodb.mongod"
+    start_db_process = f"exec --unit {unit.name} snap start charmed-mongodb.mongod"
     await ops_test.juju(*start_db_process.split())
 
 
diff --git a/tests/integration/ha_tests/test_ha.py b/tests/integration/ha_tests/test_ha.py
index fd976d8df..9edd2b812 100644
--- a/tests/integration/ha_tests/test_ha.py
+++ b/tests/integration/ha_tests/test_ha.py
@@ -69,7 +69,7 @@ async def change_logging(ops_test: OpsTest):
         time.sleep(15)
 
         # remove the log file as to not clog up space on the replicas.
-        rm_cmd = f"run --unit {unit.name} rm {helpers.MONGODB_LOG_PATH}"
+        rm_cmd = f"exec --unit {unit.name} rm {helpers.MONGODB_LOG_PATH}"
         await ops_test.juju(*rm_cmd.split())
 
 
diff --git a/tests/integration/relation_tests/legacy_relations/helpers.py b/tests/integration/relation_tests/legacy_relations/helpers.py
index f56866962..9bb27b3fe 100644
--- a/tests/integration/relation_tests/legacy_relations/helpers.py
+++ b/tests/integration/relation_tests/legacy_relations/helpers.py
@@ -159,7 +159,7 @@ async def check_tls(ops_test: OpsTest, unit: ops.model.Unit, enabled: bool) -> b
         ):
             with attempt:
                 mongod_tls_check = await mongo_tls_command(ops_test)
-                check_tls_cmd = f"run --unit {unit.name} -- {mongod_tls_check}"
+                check_tls_cmd = f"exec --unit {unit.name} -- {mongod_tls_check}"
                 return_code, _, _ = await ops_test.juju(*check_tls_cmd.split())
                 tls_enabled = return_code == 0
                 if enabled != tls_enabled:
diff --git a/tests/integration/relation_tests/legacy_relations/test_charm_legacy_relations.py b/tests/integration/relation_tests/legacy_relations/test_charm_legacy_relations.py
index cd0857f46..11e358c40 100644
--- a/tests/integration/relation_tests/legacy_relations/test_charm_legacy_relations.py
+++ b/tests/integration/relation_tests/legacy_relations/test_charm_legacy_relations.py
@@ -133,7 +133,7 @@ async def test_add_unit_joins_without_auth(ops_test: OpsTest):
     """Verify scaling mongodb with legacy relations supports no auth."""
     await ops_test.model.applications[DATABASE_APP_NAME].add_unit(count=1)
     await ops_test.model.wait_for_idle(
-        apps=[DATABASE_APP_NAME], status="active", timeout=1000, wait_for_units=3
+        apps=[DATABASE_APP_NAME], status="active", timeout=1000, wait_for_exact_units=3
     )
 
     # verify auth is still disabled
diff --git a/tests/integration/relation_tests/new_relations/test_charm_relations.py b/tests/integration/relation_tests/new_relations/test_charm_relations.py
index 532cd5a96..e3d7920bd 100644
--- a/tests/integration/relation_tests/new_relations/test_charm_relations.py
+++ b/tests/integration/relation_tests/new_relations/test_charm_relations.py
@@ -49,7 +49,7 @@ async def test_deploy_charms(ops_test: OpsTest, application_charm, database_char
             application_name=ANOTHER_DATABASE_APP_NAME,
         ),
     )
-    await ops_test.model.wait_for_idle(apps=APP_NAMES, status="active", wait_for_units=1)
+    await ops_test.model.wait_for_idle(apps=APP_NAMES, status="active", wait_for_at_least_units=1)
 
 
 @pytest.mark.abort_on_fail