diff --git a/tests/integration/helpers/cluster.py b/tests/integration/helpers/cluster.py
index be37ada9a299..128cce63169d 100644
--- a/tests/integration/helpers/cluster.py
+++ b/tests/integration/helpers/cluster.py
@@ -73,7 +73,8 @@
 # Minimum version we use in integration tests to check compatibility with old releases
 # Keep in mind that we only support upgrading between releases that are at most 1 year different.
 # This means that this minimum need to be, at least, 1 year older than the current release
-CLICKHOUSE_CI_MIN_TESTED_VERSION = "v23.3.19.33.altinitystable"
+# NOTE(vnemkov): this is a docker tag, make sure it doesn't include initial 'v'
+CLICKHOUSE_CI_MIN_TESTED_VERSION = "23.3.19.33.altinitystable"
 
 
 # to create docker-compose env file
diff --git a/tests/integration/test_distributed_inter_server_secret/configs/users.d/new_user.xml b/tests/integration/test_distributed_inter_server_secret/configs/users.d/new_user.xml
new file mode 100644
index 000000000000..a747d61a0dd9
--- /dev/null
+++ b/tests/integration/test_distributed_inter_server_secret/configs/users.d/new_user.xml
@@ -0,0 +1,12 @@
+<clickhouse>
+    <users>
+        <new_user>
+            <password></password>
+            <networks>
+                <ip>::/0</ip>
+            </networks>
+            <profile>default</profile>
+            <quota>default</quota>
+        </new_user>
+    </users>
+</clickhouse>
diff --git a/tests/integration/test_distributed_inter_server_secret/test.py b/tests/integration/test_distributed_inter_server_secret/test.py
index 44ec6f2156d3..3bfb7642c9ce 100644
--- a/tests/integration/test_distributed_inter_server_secret/test.py
+++ b/tests/integration/test_distributed_inter_server_secret/test.py
@@ -12,12 +12,17 @@
 cluster = ClickHouseCluster(__file__)
 
 
-def make_instance(name, cfg, *args, **kwargs):
+def make_instance(name, *args, **kwargs):
+    main_configs = kwargs.pop("main_configs", [])
+    main_configs.append("configs/remote_servers.xml")
+    user_configs = kwargs.pop("user_configs", [])
+    user_configs.append("configs/users.xml")
+
     return cluster.add_instance(
         name,
         with_zookeeper=True,
-        main_configs=["configs/remote_servers.xml", cfg],
-        user_configs=["configs/users.xml"],
+        main_configs=main_configs,
+        user_configs=user_configs,
         *args,
         **kwargs,
     )
diff --git a/tests/integration/test_prometheus_endpoint/test.py b/tests/integration/test_prometheus_endpoint/test.py
index f140ebdfbe78..c1f04497b556 100644
--- a/tests/integration/test_prometheus_endpoint/test.py
+++ b/tests/integration/test_prometheus_endpoint/test.py
@@ -28,7 +28,7 @@ def parse_response_line(line):
 
     if line.startswith("#"):
         return {}
-    match = re.match("^([a-zA-Z_:][a-zA-Z0-9_:]+)(\{.*\})? -?(\d)", line)
+    match = re.match(r"^([a-zA-Z_:][a-zA-Z0-9_:]+)(\{.*\})? -?(\d)", line)
     assert match, line
     name, _, val = match.groups()
     return {name: int(val)}
diff --git a/tests/integration/test_replicated_merge_tree_replicated_db_ttl/configs/enable_parallel_replicas.xml b/tests/integration/test_replicated_merge_tree_replicated_db_ttl/configs/enable_parallel_replicas.xml
index c654074740a5..7854114d582b 100644
--- a/tests/integration/test_replicated_merge_tree_replicated_db_ttl/configs/enable_parallel_replicas.xml
+++ b/tests/integration/test_replicated_merge_tree_replicated_db_ttl/configs/enable_parallel_replicas.xml
@@ -3,6 +3,7 @@
         <default>
             <allow_experimental_analyzer>1</allow_experimental_analyzer>
             <allow_experimental_parallel_reading_from_replicas>1</allow_experimental_parallel_reading_from_replicas>
+            <allow_experimental_database_replicated>1</allow_experimental_database_replicated>
             <cluster_for_parallel_replicas>default</cluster_for_parallel_replicas>
             <max_parallel_replicas>100</max_parallel_replicas>
             <use_hedged_requests>0</use_hedged_requests>
diff --git a/tests/integration/test_storage_s3_queue/configs/users_old.xml b/tests/integration/test_storage_s3_queue/configs/users_old.xml
new file mode 100644
index 000000000000..227dbe9bde5b
--- /dev/null
+++ b/tests/integration/test_storage_s3_queue/configs/users_old.xml
@@ -0,0 +1,11 @@
+<clickhouse>
+    <profiles>
+        <default>
+            <stream_like_engine_allow_direct_select>1</stream_like_engine_allow_direct_select>
+            <s3queue_enable_logging_to_s3queue_log>1</s3queue_enable_logging_to_s3queue_log>
+            <!-- Used for pre-24.3 version, where this particular option is not available -->
+            <!-- <s3queue_allow_experimental_sharded_mode>1</s3queue_allow_experimental_sharded_mode> -->
+            <allow_experimental_s3queue>1</allow_experimental_s3queue>
+        </default>
+    </profiles>
+</clickhouse>
diff --git a/tests/integration/test_storage_s3_queue/test.py b/tests/integration/test_storage_s3_queue/test.py
index abad97ba8cf2..4100ef195f02 100644
--- a/tests/integration/test_storage_s3_queue/test.py
+++ b/tests/integration/test_storage_s3_queue/test.py
@@ -103,9 +103,11 @@ def started_cluster():
         )
         cluster.add_instance(
             "old_instance",
+            user_configs=["configs/users_old.xml"],
             with_zookeeper=True,
-            image="altinity/clickhouse-server",
-            tag="23.8.11.29.altinitystable", #TODO: (mtkachenko) verify this substitution is ok. Originally 23.12
+            # NOTE (vnemkov) Can't use altinity/clickhouse here since 23.8 doesn't hve S3Queue (and associated settings yet)
+            image="clickhouse/clickhouse-server",
+            tag="23.12",
             stay_alive=True,
             with_installed_binary=True,
             use_old_analyzer=True,