diff --git a/tests/queries/0_stateless/01602_max_distributed_connections.reference b/tests/queries/0_stateless/01602_max_distributed_connections.reference
index e69de29bb2d..7326d960397 100644
--- a/tests/queries/0_stateless/01602_max_distributed_connections.reference
+++ b/tests/queries/0_stateless/01602_max_distributed_connections.reference
@@ -0,0 +1 @@
+Ok
diff --git a/tests/queries/0_stateless/01602_max_distributed_connections.sh b/tests/queries/0_stateless/01602_max_distributed_connections.sh
index 93c6071c091..772acb39344 100755
--- a/tests/queries/0_stateless/01602_max_distributed_connections.sh
+++ b/tests/queries/0_stateless/01602_max_distributed_connections.sh
@@ -4,13 +4,31 @@ CURDIR=$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)
 # shellcheck source=../shell_config.sh
 . "$CURDIR"/../shell_config.sh
 
-common_opts=(
-    "--format=Null"
+# We check that even if max_threads is small, the setting max_distributed_connections
+# will allow to process queries on multiple shards concurrently.
 
-    "--max_threads=1"
-    "--max_distributed_connections=3"
-)
+# We do sleep 1.5 seconds on ten machines.
+# If concurrency is one (bad) the query will take at least 15 seconds and the following loops are guaranteed to be infinite.
+# If concurrency is 10 (good), the query may take less than 10 second with non-zero probability
+#  and the following loops will finish with probability 1 assuming independent random variables.
 
-# NOTE: the test use higher timeout to avoid flakiness.
-timeout 9s ${CLICKHOUSE_CLIENT} "$@" "${common_opts[@]}" -q "select sleep(3) from remote('127.{1,2,3,4,5}', system.one)" --prefer_localhost_replica=0
-timeout 9s ${CLICKHOUSE_CLIENT} "$@" "${common_opts[@]}" -q "select sleep(3) from remote('127.{1,2,3,4,5}', system.one)" --prefer_localhost_replica=1
+while true; do
+    timeout 10 ${CLICKHOUSE_CLIENT} --max_threads 1 --max_distributed_connections 10 --query "
+        SELECT sleep(1.5) FROM remote('127.{1..10}', system.one) FORMAT Null" --prefer_localhost_replica=0 && break
+done
+
+while true; do
+    timeout 10 ${CLICKHOUSE_CLIENT} --max_threads 1 --max_distributed_connections 10 --query "
+        SELECT sleep(1.5) FROM remote('127.{1..10}', system.one) FORMAT Null" --prefer_localhost_replica=1 && break
+done
+
+# If max_distributed_connections is low and async_socket_for_remote is disabled,
+#  the concurrency of distributed queries will be also low.
+
+timeout 1 ${CLICKHOUSE_CLIENT} --max_threads 1 --max_distributed_connections 1 --async_socket_for_remote 0 --query "
+    SELECT sleep(0.15) FROM remote('127.{1..10}', system.one) FORMAT Null" --prefer_localhost_replica=0 && echo 'Fail'
+
+timeout 1 ${CLICKHOUSE_CLIENT} --max_threads 1 --max_distributed_connections 1 --async_socket_for_remote 0 --query "
+    SELECT sleep(0.15) FROM remote('127.{1..10}', system.one) FORMAT Null" --prefer_localhost_replica=1 && echo 'Fail'
+
+echo 'Ok'