diff --git a/src/Databases/PostgreSQL/fetchPostgreSQLTableStructure.cpp b/src/Databases/PostgreSQL/fetchPostgreSQLTableStructure.cpp
index 5268dbcb59f..29105142029 100644
--- a/src/Databases/PostgreSQL/fetchPostgreSQLTableStructure.cpp
+++ b/src/Databases/PostgreSQL/fetchPostgreSQLTableStructure.cpp
@@ -256,7 +256,7 @@ PostgreSQLTableStructure::ColumnsInfoPtr readNamesAndTypesList(
             {
                 throw Exception(
                     ErrorCodes::BAD_ARGUMENTS,
-                    "PostgreSQL cannot infer dimensions of an empty array: {}.{}",
+                    "PostgreSQL cannot infer dimensions of an empty array: {}.{}. Make sure no empty array values in the first row.",
                     postgres_table,
                     postgres_column);
             }
diff --git a/tests/integration/test_storage_postgresql/test.py b/tests/integration/test_storage_postgresql/test.py
index 78bb1167d79..b31cef826ae 100644
--- a/tests/integration/test_storage_postgresql/test.py
+++ b/tests/integration/test_storage_postgresql/test.py
@@ -267,7 +267,7 @@ def test_postgres_array_ndim_error_messges(started_cluster):
         assert False
     except Exception as error:
         assert (
-            'PostgreSQL cannot infer dimensions of an empty array: array_ndim_view."Mixed-case with spaces"'
+            'PostgreSQL cannot infer dimensions of an empty array: array_ndim_view."Mixed-case with spaces". Make sure no empty array values in the first row.'
             in str(error)
         )
 
diff --git a/tests/queries/0_stateless/01290_max_execution_speed_distributed.reference b/tests/queries/0_stateless/01290_max_execution_speed_distributed.reference
index ad0e80d8e69..4646cfab789 100644
--- a/tests/queries/0_stateless/01290_max_execution_speed_distributed.reference
+++ b/tests/queries/0_stateless/01290_max_execution_speed_distributed.reference
@@ -1,3 +1,3 @@
-2000000
+200000
 1
 1
diff --git a/tests/queries/0_stateless/01290_max_execution_speed_distributed.sql b/tests/queries/0_stateless/01290_max_execution_speed_distributed.sql
index d0dc554f425..2994d6d3ff3 100644
--- a/tests/queries/0_stateless/01290_max_execution_speed_distributed.sql
+++ b/tests/queries/0_stateless/01290_max_execution_speed_distributed.sql
@@ -1,15 +1,12 @@
 -- Tags: distributed
 
-SET max_execution_speed = 1000000;
-SET timeout_before_checking_execution_speed = 0;
-SET max_block_size = 100;
-
 SET log_queries=1;
 
 CREATE TEMPORARY TABLE times (t DateTime);
 
 INSERT INTO times SELECT now();
-SELECT count('special query for 01290_max_execution_speed_distributed') FROM remote('127.0.0.{2,3}', numbers(1000000));
+SELECT count('special query for 01290_max_execution_speed_distributed') FROM remote('127.0.0.{2,3}', numbers(100000))
+SETTINGS max_execution_speed = 100000, timeout_before_checking_execution_speed = 0, max_block_size = 100;
 INSERT INTO times SELECT now();
 
 SELECT max(t) - min(t) >= 1 FROM times;
@@ -21,6 +18,7 @@ FROM system.query_log
 WHERE
     current_database = currentDatabase() AND
     event_date >= yesterday() AND
+    event_time >= now() - INTERVAL '5 MINUTES' AND -- time limit for tests not marked `long` is 3 minutes, 5 should be more than enough
     query LIKE '%special query for 01290_max_execution_speed_distributed%' AND
     query NOT LIKE '%system.query_log%' AND
     type = 2;
diff --git a/tests/queries/0_stateless/03271_ghdata_object_to_json_alter.sh b/tests/queries/0_stateless/03271_ghdata_object_to_json_alter.sh
index fc217780aa3..5b838fed0e6 100755
--- a/tests/queries/0_stateless/03271_ghdata_object_to_json_alter.sh
+++ b/tests/queries/0_stateless/03271_ghdata_object_to_json_alter.sh
@@ -1,5 +1,6 @@
 #!/usr/bin/env bash
-# Tags: no-fasttest, long
+# Tags: no-fasttest, long, no-s3-storage
+# ^ no-s3-storage: too slow
 
 CUR_DIR=$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)
 # shellcheck source=../shell_config.sh