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 a6f67a433d2..c1fc8ffa2a4 100644
--- a/tests/queries/0_stateless/01290_max_execution_speed_distributed.sql
+++ b/tests/queries/0_stateless/01290_max_execution_speed_distributed.sql
@@ -9,19 +9,19 @@ 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() FROM remote('127.0.0.{2,3}', numbers(1000000)) SETTINGS log_comment='01290_8ca5d52f-8582-4ee3-8674-351c76d67b8c';
 INSERT INTO times SELECT now();
 
 SELECT max(t) - min(t) >= 1 FROM times;
 
 -- Check that the query was also throttled on "remote" servers.
 SYSTEM FLUSH LOGS;
-SELECT DISTINCT query_duration_ms >= 500
+SELECT COUNT()
 FROM system.query_log
 WHERE
     current_database = currentDatabase() AND
     event_date >= yesterday() AND
-    query LIKE '%special query for 01290_max_execution_speed_distributed%' AND
-    query NOT LIKE '%system.query_log%' AND
-    type = 'QueryFinish'
-SETTINGS max_threads = 0; -- to avoid TOO_SLOW error while executing the query
+    log_comment = '01290_8ca5d52f-8582-4ee3-8674-351c76d67b8c' AND
+    type = 'QueryFinish' AND
+    query_duration_ms >= 500
+SETTINGS max_threads = 0;
diff --git a/tests/queries/0_stateless/03231_pr_max_execution_time.sql b/tests/queries/0_stateless/03231_pr_max_execution_time.sql
index b7b6d436f26..09e01673727 100644
--- a/tests/queries/0_stateless/03231_pr_max_execution_time.sql
+++ b/tests/queries/0_stateless/03231_pr_max_execution_time.sql
@@ -8,8 +8,9 @@ CREATE TABLE 03231_max_execution_time_t
 ENGINE = ReplicatedMergeTree('/clickhouse/{database}/03231_max_execution_time', 'r1')
 ORDER BY (key, value);
 
-SET max_rows_to_read = 100_000_000; -- to avoid DB::Exception: Limit for rows (controlled by 'max_rows_to_read' setting) exceeded, max rows: 20.00 million, current rows: 100.00 million. (TOO_MANY_ROWS)
-INSERT INTO 03231_max_execution_time_t SELECT number, toString(number) FROM numbers_mt(100_000_000) SETTINGS max_threads=0, max_insert_threads=0;
+SET max_rows_to_read = 20_000_000;
+SYSTEM STOP MERGES 03231_max_execution_time_t;
+INSERT INTO 03231_max_execution_time_t SELECT number, toString(number) FROM numbers_mt(20_000_000) SETTINGS max_threads=0, max_insert_threads=0;
 
 SET allow_experimental_parallel_reading_from_replicas = 2, max_parallel_replicas = 3, cluster_for_parallel_replicas='test_cluster_one_shard_three_replicas_localhost';
 SET use_query_cache = false;