diff --git a/tests/queries/0_stateless/00926_adaptive_index_granularity_versioned_collapsing_merge_tree.reference b/tests/queries/0_stateless/00926_adaptive_index_granularity_versioned_collapsing_merge_tree.reference
index 067189f73fc..f93aae0225a 100644
--- a/tests/queries/0_stateless/00926_adaptive_index_granularity_versioned_collapsing_merge_tree.reference
+++ b/tests/queries/0_stateless/00926_adaptive_index_granularity_versioned_collapsing_merge_tree.reference
@@ -6,11 +6,9 @@
 4
 1
 0
-0
 6
 2
 -----
 6
 3
 0
-0
diff --git a/tests/queries/0_stateless/00926_adaptive_index_granularity_versioned_collapsing_merge_tree.sql b/tests/queries/0_stateless/00926_adaptive_index_granularity_versioned_collapsing_merge_tree.sql
index 4d4dbda922d..44dd0412aea 100644
--- a/tests/queries/0_stateless/00926_adaptive_index_granularity_versioned_collapsing_merge_tree.sql
+++ b/tests/queries/0_stateless/00926_adaptive_index_granularity_versioned_collapsing_merge_tree.sql
@@ -62,7 +62,11 @@ OPTIMIZE TABLE four_rows_per_granule FINAL;
 
 SELECT COUNT(*) FROM four_rows_per_granule;
 
-SELECT distinct(marks) from system.parts WHERE table = 'four_rows_per_granule' and database=currentDatabase() and active=1;
+-- We expect zero marks here, so we might get zero rows if all the parts were
+-- deleted already. This can happen in parallel runs where there may be a long delay
+-- between queries. So we must write the query in such a way that it always returns
+-- zero rows if OK.
+SELECT distinct(marks) d from system.parts WHERE table = 'four_rows_per_granule' and database=currentDatabase() and active=1 having d > 0;
 
 INSERT INTO four_rows_per_granule (p, k, v1, v2, Sign, Version) VALUES ('2018-05-15', 1, 1000, 2000, 1, 1), ('2018-05-16', 2, 3000, 4000, 1, 1), ('2018-05-17', 3, 5000, 6000, 1, 1), ('2018-05-18', 4, 7000, 8000, 1, 1);
 
@@ -120,6 +124,10 @@ OPTIMIZE TABLE six_rows_per_granule FINAL;
 
 SELECT COUNT(*) FROM six_rows_per_granule;
 
-SELECT distinct(marks) from system.parts WHERE table = 'six_rows_per_granule' and database=currentDatabase() and active=1;
+-- We expect zero marks here, so we might get zero rows if all the parts were
+-- deleted already. This can happen in parallel runs where there may be a long delay
+-- between queries. So we must write the query in such a way that it always returns
+-- zero rows if OK.
+SELECT distinct(marks) d from system.parts WHERE table = 'six_rows_per_granule' and database=currentDatabase() and active=1 having d > 0;
 
 DROP TABLE IF EXISTS six_rows_per_granule;
diff --git a/tests/queries/skip_list.json b/tests/queries/skip_list.json
index df2090325a3..bdb5c5bd319 100644
--- a/tests/queries/skip_list.json
+++ b/tests/queries/skip_list.json
@@ -641,6 +641,7 @@
         "01542_dictionary_load_exception_race",
         "01545_system_errors", // looks at the difference of values in system.errors
         "01560_optimize_on_insert_zookeeper",
+        "01563_distributed_query_finish", // looks at system.errors which is global
         "01575_disable_detach_table_of_dictionary",
         "01593_concurrent_alter_mutations_kill",
         "01593_concurrent_alter_mutations_kill_many_replicas",