diff --git a/tests/queries/0_stateless/03166_optimize_row_order_during_insert_equivalence_classes.reference b/tests/queries/0_stateless/03166_optimize_row_order_during_insert_equivalence_classes.reference
new file mode 100644
index 00000000000..922371c4d38
--- /dev/null
+++ b/tests/queries/0_stateless/03166_optimize_row_order_during_insert_equivalence_classes.reference
@@ -0,0 +1,16 @@
+AB	1	9.81	0
+A\0	0	2.7	1
+A\0	1	2.7	1
+B\0	0	2.7	1
+B\0	1	2.7	1
+A\0	1	42	1
+B\0	0	42	1
+A\0	0	3.14	\N
+B\0	-1	3.14	\N
+B\0	2	3.14	\N
+AB	0	42	\N
+AB	0	42	\N
+B\0	0	42	\N
+A\0	1	42	\N
+A\0	1	42	\N
+B\0	1	42	\N
diff --git a/tests/queries/0_stateless/03166_optimize_row_order_during_insert_equivalence_classes.sql b/tests/queries/0_stateless/03166_optimize_row_order_during_insert_equivalence_classes.sql
new file mode 100644
index 00000000000..6c04093023c
--- /dev/null
+++ b/tests/queries/0_stateless/03166_optimize_row_order_during_insert_equivalence_classes.sql
@@ -0,0 +1,15 @@
+-- Checks that RowOptimizer correctly selects the order for columns according to cardinality in each equivalence class obtained using SortDescription.
+-- There are two columns in the SortDescription: {flag, money} in this order.
+-- So there are 5 equivalence classes: {9.81, 9}, {2.7, 1}, {42, 1}, {3.14, Null}, {42, Null}.
+-- For the first three of them cardinalities of the other 2 columns are equal, so they are sorted in order {0, 1} in these classes.
+-- In the fourth class cardinalities: {name : 2, timestamp : 3}, so they are sorted in order {name, timestamp} in this class.
+-- In the fifth class cardinalities: {name : 3, timestamp : 2}, so they are sorted in order {timestamp, name} in this class.
+
+DROP TABLE IF EXISTS tab;
+
+CREATE TABLE tab (name FixedString(2), timestamp Float32, money Float64, flag Nullable(Int32)) ENGINE = MergeTree ORDER BY (flag, money) SETTINGS allow_experimental_optimized_row_order = True, allow_nullable_key = True;
+INSERT INTO tab VALUES ('AB', 0, 42, Null), ('AB', 0, 42, Null), ('A', 1, 42, Null), ('AB', 1, 9.81, 0), ('B', 0, 42, Null), ('B', -1, 3.14, Null), ('B', 1, 2.7, 1), ('B', 0, 42, 1), ('A', 1, 42, 1), ('B', 1, 42, Null), ('B', 0, 2.7, 1), ('A', 0, 2.7, 1), ('B', 2, 3.14, Null), ('A', 0, 3.14, Null), ('A', 1, 2.7, 1), ('A', 1, 42, Null);
+
+SELECT * FROM tab SETTINGS max_threads=1;
+
+DROP TABLE tab;