diff --git a/docker/test/stateful/run.sh b/docker/test/stateful/run.sh
index 77dc61e6cd0..861e17848a4 100755
--- a/docker/test/stateful/run.sh
+++ b/docker/test/stateful/run.sh
@@ -115,7 +115,7 @@ function run_tests()
     fi
 
     set +e
-    clickhouse-test --testname --shard --zookeeper --check-zookeeper-session --no-stateless --hung-check --print-time \
+    clickhouse-test -j 2 --testname --shard --zookeeper --check-zookeeper-session --no-stateless --hung-check --print-time \
         --skip 00168_parallel_processing_on_replicas "${ADDITIONAL_OPTIONS[@]}" \
         "$SKIP_TESTS_OPTION" 2>&1 | ts '%Y-%m-%d %H:%M:%S' | tee test_output/test_result.txt
 
diff --git a/tests/clickhouse-test b/tests/clickhouse-test
index 5f9ab01cdcc..6d1c7a12cc4 100755
--- a/tests/clickhouse-test
+++ b/tests/clickhouse-test
@@ -52,6 +52,7 @@ MESSAGES_TO_RETRY = [
     "DB::Exception: New table appeared in database being dropped or detached. Try again",
     "is already started to be removing by another replica right now",
     "DB::Exception: Cannot enqueue query",
+    "environment: line 1: wait_for: No record of process", # Something weird from bash internals, let's just retry
     "is executing longer than distributed_ddl_task_timeout" # FIXME
 ]
 
diff --git a/tests/queries/0_stateless/00385_storage_file_and_clickhouse-local_app_long.sh b/tests/queries/0_stateless/00385_storage_file_and_clickhouse-local_app_long.sh
index a78cdd445cb..b6cc270994f 100755
--- a/tests/queries/0_stateless/00385_storage_file_and_clickhouse-local_app_long.sh
+++ b/tests/queries/0_stateless/00385_storage_file_and_clickhouse-local_app_long.sh
@@ -1,5 +1,5 @@
 #!/usr/bin/env bash
-# Tags: long
+# Tags: long, no-random-settings
 
 set -e
 
diff --git a/tests/queries/1_stateful/00140_rename.sql b/tests/queries/1_stateful/00140_rename.sql
index 9702d00a4d5..88671d51027 100644
--- a/tests/queries/1_stateful/00140_rename.sql
+++ b/tests/queries/1_stateful/00140_rename.sql
@@ -1,4 +1,4 @@
--- Tags: no-replicated-database
+-- Tags: no-replicated-database, no-parallel
 -- Tag no-replicated-database: Does not support renaming of multiple tables in single query
 
 RENAME TABLE test.hits TO test.visits_tmp, test.visits TO test.hits, test.visits_tmp TO test.visits;
diff --git a/tests/queries/1_stateful/00152_insert_different_granularity.sql b/tests/queries/1_stateful/00152_insert_different_granularity.sql
index da99173ed96..6415cdad8a5 100644
--- a/tests/queries/1_stateful/00152_insert_different_granularity.sql
+++ b/tests/queries/1_stateful/00152_insert_different_granularity.sql
@@ -1,4 +1,4 @@
--- Tags: no-tsan, no-replicated-database
+-- Tags: no-tsan, no-replicated-database, no-parallel
 -- Tag no-replicated-database: Fails due to additional replicas or shards
 
 DROP TABLE IF EXISTS fixed_granularity_table;
diff --git a/tests/queries/1_stateful/00170_s3_cache.reference b/tests/queries/1_stateful/00170_s3_cache.reference
index 9c9c3bc537f..aeb7022b3f7 100644
--- a/tests/queries/1_stateful/00170_s3_cache.reference
+++ b/tests/queries/1_stateful/00170_s3_cache.reference
@@ -1,4 +1,5 @@
 -- { echo }
+
 SET max_memory_usage='20G';
 SELECT count() FROM test.hits_s3;
 8873898
diff --git a/tests/queries/1_stateful/00170_s3_cache.sql b/tests/queries/1_stateful/00170_s3_cache.sql
index af3fd402596..d4837a1a800 100644
--- a/tests/queries/1_stateful/00170_s3_cache.sql
+++ b/tests/queries/1_stateful/00170_s3_cache.sql
@@ -1,4 +1,7 @@
+-- Tags: no-parallel
+
 -- { echo }
+
 SET max_memory_usage='20G';
 SELECT count() FROM test.hits_s3;
 SELECT count() FROM test.hits_s3 WHERE AdvEngineID != 0;