diff --git a/pgtype/array_codec_test.go b/pgtype/array_codec_test.go
index 65289d04..9da027e8 100644
--- a/pgtype/array_codec_test.go
+++ b/pgtype/array_codec_test.go
@@ -6,6 +6,7 @@ import (
 
 	pgx "github.com/jackc/pgx/v5"
 	"github.com/jackc/pgx/v5/pgtype"
+	"github.com/jackc/pgx/v5/pgxtest"
 	"github.com/stretchr/testify/assert"
 	"github.com/stretchr/testify/require"
 )
@@ -70,7 +71,12 @@ func TestArrayCodecFlatArray(t *testing.T) {
 }
 
 func TestArrayCodecArray(t *testing.T) {
-	defaultConnTestRunner.RunTest(context.Background(), t, func(ctx context.Context, t testing.TB, conn *pgx.Conn) {
+	ctr := defaultConnTestRunner
+	ctr.AfterConnect = func(ctx context.Context, t testing.TB, conn *pgx.Conn) {
+		pgxtest.SkipCockroachDB(t, conn, "Server does not support multi-dimensional arrays")
+	}
+
+	ctr.RunTest(context.Background(), t, func(ctx context.Context, t testing.TB, conn *pgx.Conn) {
 		for i, tt := range []struct {
 			expected any
 		}{
diff --git a/stdlib/sql_test.go b/stdlib/sql_test.go
index faa4a0cb..9106df62 100644
--- a/stdlib/sql_test.go
+++ b/stdlib/sql_test.go
@@ -398,6 +398,8 @@ func TestConnQueryScanArray(t *testing.T) {
 
 func TestConnQueryScanRange(t *testing.T) {
 	testWithAllQueryExecModes(t, func(t *testing.T, db *sql.DB) {
+		skipCockroachDB(t, db, "Server does not support int4range")
+
 		m := pgtype.NewMap()
 
 		var r pgtype.Range[pgtype.Int4]