diff --git a/tests/queries/0_stateless/00340_squashing_insert_select.sql b/tests/queries/0_stateless/00340_squashing_insert_select.sql
index 102eb061bad..6b7133c155e 100644
--- a/tests/queries/0_stateless/00340_squashing_insert_select.sql
+++ b/tests/queries/0_stateless/00340_squashing_insert_select.sql
@@ -7,6 +7,8 @@ SET max_block_size = 10000;
 SET min_insert_block_size_rows = 1000000;
 SET min_insert_block_size_bytes = 0;
 
+set max_insert_threads = 1;
+
 INSERT INTO numbers_squashed SELECT * FROM system.numbers LIMIT 10000000;
 SELECT blockSize() AS b, count() / b AS c FROM numbers_squashed GROUP BY blockSize() ORDER BY c DESC;
 
diff --git a/tests/queries/0_stateless/00804_test_delta_codec_compression.sql b/tests/queries/0_stateless/00804_test_delta_codec_compression.sql
index 01a2f53bf93..0b289ad7c1d 100644
--- a/tests/queries/0_stateless/00804_test_delta_codec_compression.sql
+++ b/tests/queries/0_stateless/00804_test_delta_codec_compression.sql
@@ -16,6 +16,8 @@ CREATE TABLE default_codec_synthetic
     id UInt64 Codec(ZSTD(3))
 ) ENGINE MergeTree() ORDER BY tuple() SETTINGS min_bytes_for_wide_part = 0, compress_marks = false, compress_primary_key = false, ratio_of_defaults_for_sparse_serialization = 1;
 
+set max_insert_threads = 1;
+
 INSERT INTO delta_codec_synthetic SELECT number FROM system.numbers LIMIT 5000000;
 INSERT INTO default_codec_synthetic SELECT number FROM system.numbers LIMIT 5000000;
 
diff --git a/tests/queries/0_stateless/01019_Buffer_and_max_memory_usage.sql b/tests/queries/0_stateless/01019_Buffer_and_max_memory_usage.sql
index 9fbc3f951fe..777effe9e81 100644
--- a/tests/queries/0_stateless/01019_Buffer_and_max_memory_usage.sql
+++ b/tests/queries/0_stateless/01019_Buffer_and_max_memory_usage.sql
@@ -25,6 +25,7 @@ CREATE TABLE buffer_ (key UInt64) Engine=Buffer(currentDatabase(), null_,
 
 SET max_memory_usage=10e6;
 SET max_block_size=100e3;
+SET max_insert_threads=1;
 
 -- Check that max_memory_usage is ignored only on flush and not on squash
 SET min_insert_block_size_bytes=9e6;
diff --git a/tests/queries/0_stateless/01201_read_single_thread_in_order.sql b/tests/queries/0_stateless/01201_read_single_thread_in_order.sql
index 24ed935a125..6e92b4aa953 100644
--- a/tests/queries/0_stateless/01201_read_single_thread_in_order.sql
+++ b/tests/queries/0_stateless/01201_read_single_thread_in_order.sql
@@ -8,7 +8,7 @@ ENGINE = MergeTree
 ORDER BY number
 SETTINGS index_granularity = 128, ratio_of_defaults_for_sparse_serialization = 1.0, index_granularity_bytes = '10Mi';
 
-SET min_insert_block_size_rows = 0, min_insert_block_size_bytes = 0;
+SET min_insert_block_size_rows = 0, min_insert_block_size_bytes = 0, max_insert_threads = 1;
 INSERT INTO t SELECT number FROM numbers(10000000);
 
 SET max_threads = 1, max_block_size = 12345;
diff --git a/tests/queries/0_stateless/02428_combinators_with_over_statement.sql b/tests/queries/0_stateless/02428_combinators_with_over_statement.sql
index 7946b997b00..2b82839d6eb 100644
--- a/tests/queries/0_stateless/02428_combinators_with_over_statement.sql
+++ b/tests/queries/0_stateless/02428_combinators_with_over_statement.sql
@@ -1,5 +1,6 @@
 drop table if exists test;
 create table test (x AggregateFunction(uniq, UInt64), y Int64) engine=Memory;
+set max_insert_threads = 1;
 insert into test select uniqState(number) as x, number as y from numbers(10) group by number order by x, y;
 select uniqStateMap(map(1, x)) OVER (PARTITION BY y) from test;
 select uniqStateForEach([x]) OVER (PARTITION BY y) from test;
diff --git a/tests/queries/0_stateless/02457_insert_select_progress_http.sh b/tests/queries/0_stateless/02457_insert_select_progress_http.sh
index ae62ee4b77e..ccf37dfb327 100755
--- a/tests/queries/0_stateless/02457_insert_select_progress_http.sh
+++ b/tests/queries/0_stateless/02457_insert_select_progress_http.sh
@@ -4,6 +4,6 @@ CURDIR=$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)
 # shellcheck source=../shell_config.sh
 . "$CURDIR"/../shell_config.sh
 
-${CLICKHOUSE_CURL} -sS "${CLICKHOUSE_URL}&send_progress_in_http_headers=1&http_headers_progress_interval_ms=0" -d @- <<< "insert into function null('_ Int') select * from numbers(5) settings max_block_size=1" -v |& {
+${CLICKHOUSE_CURL} -sS "${CLICKHOUSE_URL}&send_progress_in_http_headers=1&http_headers_progress_interval_ms=0" -d @- <<< "insert into function null('_ Int') select * from numbers(5) settings max_block_size=1, max_insert_threads=1" -v |& {
     grep -F -e X-ClickHouse-Progress: -e X-ClickHouse-Summary:  | sed 's/,\"elapsed_ns[^}]*//'
 }
diff --git a/tests/queries/0_stateless/02486_truncate_and_unexpected_parts.sql b/tests/queries/0_stateless/02486_truncate_and_unexpected_parts.sql
index 5c90313b6b8..507ac7289f5 100644
--- a/tests/queries/0_stateless/02486_truncate_and_unexpected_parts.sql
+++ b/tests/queries/0_stateless/02486_truncate_and_unexpected_parts.sql
@@ -5,7 +5,7 @@ create table rmt1 (n int) engine=ReplicatedMergeTree('/test/02468/{database}', '
 system stop cleanup rmt;
 system stop merges rmt1;
 
-insert into rmt select * from numbers(10) settings max_block_size=1;
+insert into rmt select * from numbers(10) settings max_block_size=1, max_insert_threads=1;
 
 alter table rmt drop partition id '0';
 truncate table rmt1;
@@ -31,7 +31,7 @@ create table rmt2 (n int) engine=ReplicatedMergeTree('/test/02468/{database}2',
 
 system stop cleanup rmt;
 system stop merges rmt1;
-insert into rmt select * from numbers(10) settings max_block_size=1;
+insert into rmt select * from numbers(10) settings max_block_size=1, max_insert_threads=1;
 system sync replica rmt1 lightweight;
 
 alter table rmt replace partition id '0' from rmt2;