diff --git a/src/Storages/StorageMergeTree.cpp b/src/Storages/StorageMergeTree.cpp
index 38b9a5790e6..5a41b81252e 100644
--- a/src/Storages/StorageMergeTree.cpp
+++ b/src/Storages/StorageMergeTree.cpp
@@ -1218,7 +1218,7 @@ size_t StorageMergeTree::clearOldMutations(bool truncate)
             auto versions_it = std::lower_bound(
                 part_versions_with_names.begin(), part_versions_with_names.end(), needle);
 
-            if (versions_it != part_versions_with_names.begin())
+            if (versions_it != part_versions_with_names.begin() || !it->second.tid.isPrehistoric())
             {
                 done_count = std::distance(begin_it, it);
                 break;
@@ -1235,7 +1235,8 @@ size_t StorageMergeTree::clearOldMutations(bool truncate)
         {
             const auto & tid = it->second.tid;
             if (!tid.isPrehistoric() && !TransactionLog::instance().getCSN(tid))
-                throw Exception(ErrorCodes::LOGICAL_ERROR, "Cannot remove mutation {}, because transaction {} is not committed. It's a bug");
+                throw Exception(ErrorCodes::LOGICAL_ERROR, "Cannot remove mutation {}, because transaction {} is not committed. It's a bug",
+                                it->first, tid);
             mutations_to_delete.push_back(std::move(it->second));
             it = current_mutations_by_version.erase(it);
         }
diff --git a/tests/queries/0_stateless/01168_mutations_isolation.sh b/tests/queries/0_stateless/01168_mutations_isolation.sh
index e6049e50131..e034b467358 100755
--- a/tests/queries/0_stateless/01168_mutations_isolation.sh
+++ b/tests/queries/0_stateless/01168_mutations_isolation.sh
@@ -56,7 +56,7 @@ tx 6                                            "commit"
 tx 7 "begin transaction"
 tx 7 "select 7, n, _part from mt order by n"
 tx 8                                            "begin transaction"
-tx 8                                            "alter table mt update n = 0 where 1" &
+tx 8                                            "alter table mt update n = 0 where 1" >/dev/null &
 $CLICKHOUSE_CLIENT -q "kill mutation where database=currentDatabase() and mutation_id='mutation_15.txt' format Null"
 wait
 tx 7 "optimize table mt final"
diff --git a/tests/queries/0_stateless/transactions.lib b/tests/queries/0_stateless/transactions.lib
index be8745e68a5..d4d349d8827 100755
--- a/tests/queries/0_stateless/transactions.lib
+++ b/tests/queries/0_stateless/transactions.lib
@@ -1,6 +1,8 @@
 #!/usr/bin/env bash
 
-# Useful to run
+# shellcheck disable=SC2015
+
+# Useful to run queries in parallel sessions
 function tx()
 {
     tx_num=$1
@@ -14,12 +16,24 @@ function tx()
     ${CLICKHOUSE_CURL} -m 60 -sSk "$url" --data "$query" | sed "s/^/tx$tx_num\t/"
 }
 
+# Waits for the last query in session to finish
 function tx_wait() {
     tx_num=$1
 
     session="${CLICKHOUSE_TEST_ZOOKEEPER_PREFIX}_tx$tx_num"
 
+    # try get pid of previous query
+    query_pid=""
+    tmp_file_name="${CLICKHOUSE_TMP}/tmp_tx_${CLICKHOUSE_TEST_ZOOKEEPER_PREFIX}"
+    query_id_and_pid=$(grep -F "$session" "$tmp_file_name" 2>/dev/null | tail -1) ||:
+    read -r query_id query_pid <<< "$query_id_and_pid" ||:
+
     # wait for previous query in transaction
+    if [ -n "$query_pid" ]; then
+        timeout 5 tail --pid=$query_pid -f /dev/null && return ||:
+    fi
+
+    # there is no pid (or maybe we got wrong one), so wait using system.processes (it's less reliable)
     count=0
     while [[ $($CLICKHOUSE_CLIENT -q "SELECT count() FROM system.processes WHERE query_id LIKE '$session%'") -gt 0 ]]; do
         sleep 0.5
@@ -31,6 +45,7 @@ function tx_wait() {
     done;
 }
 
+# Wait for previous query in session to finish, starts new one asynchronously
 function tx_async()
 {
     tx_num=$1
@@ -43,6 +58,12 @@ function tx_async()
     url_without_session="https://${CLICKHOUSE_HOST}:${CLICKHOUSE_PORT_HTTPS}/?"
     url="${url_without_session}session_id=$session&query_id=$query_id&database=$CLICKHOUSE_DATABASE"
 
+    # We cannot be sure that query will actually start execution and appear in system.processes before the next call to tx_wait
+    # Also we cannot use global map in bash to store last query_id for each tx_num, so we use tmp file...
+    tmp_file_name="${CLICKHOUSE_TMP}/tmp_tx_${CLICKHOUSE_TEST_ZOOKEEPER_PREFIX}"
+
     # run query asynchronously
     ${CLICKHOUSE_CURL} -m 60 -sSk "$url" --data "$query" | sed "s/^/tx$tx_num\t/" &
+    query_pid=$!
+    echo -e "$query_id\t$query_pid" >> "$tmp_file_name"
 }