diff --git a/integration/aggregate_documents_compat_test.go b/integration/aggregate_documents_compat_test.go
index 4137bbe4b9b5..e77b790948f0 100644
--- a/integration/aggregate_documents_compat_test.go
+++ b/integration/aggregate_documents_compat_test.go
@@ -320,6 +320,8 @@ func TestAggregateCompatOptions(t *testing.T) {
 }
 
 func TestAggregateCompatStages(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3520")
+
 	t.Parallel()
 
 	testCases := map[string]aggregateStagesCompatTestCase{
@@ -902,6 +904,8 @@ func TestAggregateCompatGroupCount(t *testing.T) {
 }
 
 func TestAggregateCompatLimit(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3520")
+
 	t.Parallel()
 
 	testCases := map[string]aggregateStagesCompatTestCase{
@@ -1243,6 +1247,8 @@ func TestAggregateCompatGroupSum(t *testing.T) {
 }
 
 func TestAggregateCompatMatch(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3520")
+
 	t.Parallel()
 
 	// TODO https://github.com/FerretDB/FerretDB/issues/2291
@@ -1505,6 +1511,8 @@ func TestAggregateCompatUnwind(t *testing.T) {
 }
 
 func TestAggregateCompatSkip(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3520")
+
 	t.Parallel()
 
 	testCases := map[string]aggregateStagesCompatTestCase{
diff --git a/integration/commands_administration_test.go b/integration/commands_administration_test.go
index 30b2705ee1b4..a05cd632645e 100644
--- a/integration/commands_administration_test.go
+++ b/integration/commands_administration_test.go
@@ -698,6 +698,8 @@ func TestCommandsAdministrationCollStatsEmpty(t *testing.T) {
 }
 
 func TestCommandsAdministrationCollStats(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3521")
+
 	t.Parallel()
 
 	ctx, collection := setup.Setup(t, shareddata.DocumentsStrings)
@@ -730,6 +732,8 @@ func TestCommandsAdministrationCollStats(t *testing.T) {
 }
 
 func TestCommandsAdministrationCollStatsWithScale(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3521")
+
 	t.Parallel()
 
 	ctx, collection := setup.Setup(t, shareddata.DocumentsStrings)
@@ -777,6 +781,8 @@ func TestCommandsAdministrationCollStatsCount(t *testing.T) {
 }
 
 func TestCommandsAdministrationDataSize(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3521")
+
 	t.Parallel()
 
 	t.Run("Existing", func(t *testing.T) {
diff --git a/integration/query_array_compat_test.go b/integration/query_array_compat_test.go
index 92eb4cd767c4..0d0cc444396f 100644
--- a/integration/query_array_compat_test.go
+++ b/integration/query_array_compat_test.go
@@ -20,6 +20,8 @@ import (
 
 	"go.mongodb.org/mongo-driver/bson"
 	"go.mongodb.org/mongo-driver/bson/primitive"
+
+	"github.com/FerretDB/FerretDB/integration/setup"
 )
 
 func TestQueryArrayCompatSize(t *testing.T) {
@@ -133,6 +135,8 @@ func TestQueryArrayCompatDotNotation(t *testing.T) {
 }
 
 func TestQueryArrayCompatElemMatch(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3526")
+
 	t.Parallel()
 
 	testCases := map[string]queryCompatTestCase{
diff --git a/integration/query_comparison_compat_test.go b/integration/query_comparison_compat_test.go
index 5d4f6e039267..2280ef97eee0 100644
--- a/integration/query_comparison_compat_test.go
+++ b/integration/query_comparison_compat_test.go
@@ -22,11 +22,14 @@ import (
 	"go.mongodb.org/mongo-driver/bson"
 	"go.mongodb.org/mongo-driver/bson/primitive"
 
+	"github.com/FerretDB/FerretDB/integration/setup"
 	"github.com/FerretDB/FerretDB/integration/shareddata"
 	"github.com/FerretDB/FerretDB/internal/util/must"
 )
 
 func TestQueryComparisonCompatImplicit(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3526")
+
 	t.Parallel()
 
 	testCases := map[string]queryCompatTestCase{
@@ -291,6 +294,8 @@ func TestQueryComparisonCompatImplicit(t *testing.T) {
 }
 
 func TestQueryComparisonCompatEq(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3526")
+
 	t.Parallel()
 
 	testCases := map[string]queryCompatTestCase{
@@ -1172,6 +1177,8 @@ func TestQueryComparisonCompatIn(t *testing.T) {
 }
 
 func TestQueryComparisonCompatNe(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3526")
+
 	t.Parallel()
 
 	testCases := map[string]queryCompatTestCase{
@@ -1389,6 +1396,8 @@ func TestQueryComparisonCompatNe(t *testing.T) {
 }
 
 func TestQueryComparisonCompatMultipleOperators(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3526")
+
 	t.Parallel()
 
 	var scalarDataTypesFilter bson.A
diff --git a/integration/query_compat_test.go b/integration/query_compat_test.go
index 2384cb6a63d0..1178b9778226 100644
--- a/integration/query_compat_test.go
+++ b/integration/query_compat_test.go
@@ -193,6 +193,8 @@ func testQueryCompat(t *testing.T, testCases map[string]queryCompatTestCase) {
 }
 
 func TestQueryCompatFilter(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3526")
+
 	t.Parallel()
 
 	testCases := map[string]queryCompatTestCase{
diff --git a/integration/query_projection_compat_test.go b/integration/query_projection_compat_test.go
index 9beb92a59f9a..2650ba792cf8 100644
--- a/integration/query_projection_compat_test.go
+++ b/integration/query_projection_compat_test.go
@@ -22,6 +22,7 @@ import (
 	"go.mongodb.org/mongo-driver/bson"
 	"go.mongodb.org/mongo-driver/bson/primitive"
 
+	"github.com/FerretDB/FerretDB/integration/setup"
 	"github.com/FerretDB/FerretDB/integration/shareddata"
 )
 
@@ -223,6 +224,8 @@ func TestQueryProjectionCompat(t *testing.T) {
 }
 
 func TestQueryProjectionPositionalOperatorCompat(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3526")
+
 	t.Parallel()
 
 	// TODO https://github.com/FerretDB/FerretDB/issues/3053
diff --git a/integration/query_test.go b/integration/query_test.go
index 3a152a8c54b6..b00d1033cbdb 100644
--- a/integration/query_test.go
+++ b/integration/query_test.go
@@ -821,6 +821,8 @@ func TestQueryCommandSingleBatch(t *testing.T) {
 }
 
 func TestQueryCommandLimitPushDown(t *testing.T) {
+	setup.SkipForNewPg(t, "https://github.com/FerretDB/FerretDB/issues/3416")
+
 	t.Parallel()
 
 	// must use a collection of documents which does not support query pushdown to test limit pushdown
diff --git a/integration/setup/client.go b/integration/setup/client.go
index b770d31ee34c..6e4992782ffa 100644
--- a/integration/setup/client.go
+++ b/integration/setup/client.go
@@ -39,9 +39,12 @@ func makeClient(ctx context.Context, uri string) (*mongo.Client, error) {
 		return nil, lazyerrors.Error(err)
 	}
 
-	if err = client.Ping(ctx, nil); err != nil {
-		return nil, lazyerrors.Error(err)
-	}
+	// When too many connections are open, PostgreSQL returns an error,
+	// but this error is hanging (panic in setupClient doesn't immediately stop the test).
+	// TODO https://github.com/FerretDB/FerretDB/issues/3535
+	//if err = client.Ping(ctx, nil); err != nil {
+	//	return nil, lazyerrors.Error(err)
+	//}
 
 	return client, nil
 }
diff --git a/integration/setup/test_helpers.go b/integration/setup/test_helpers.go
index 383cbf087450..6246b3e1a896 100644
--- a/integration/setup/test_helpers.go
+++ b/integration/setup/test_helpers.go
@@ -36,6 +36,15 @@ func IsOldPg(tb testtb.TB) bool {
 	return *targetBackendF == "ferretdb-pg" && !*useNewPgF
 }
 
+// IsNewPg returns true if the current test is running for new PostgreSQL handler.
+//
+// This function should not be used lightly and always with an reason provided.
+// It should be removed when a new PG handler is fully supported.
+// TODO https://github.com/FerretDB/FerretDB/issues/3435
+func IsNewPg(tb testtb.TB) bool {
+	return *targetBackendF == "ferretdb-pg" && *useNewPgF
+}
+
 // IsSQLite returns true if the current test is running for SQLite.
 //
 // This function should not be used lightly.
@@ -104,6 +113,21 @@ func SkipForOldPg(tb testtb.TB, reason string) {
 	}
 }
 
+// SkipForNewPg skips the current test for the new PG handler.
+//
+// This function should not be used lightly and always with an reason provided.
+// It should be removed when a new PG handler is fully supported.
+// TODO https://github.com/FerretDB/FerretDB/issues/3435
+func SkipForNewPg(tb testtb.TB, reason string) {
+	tb.Helper()
+
+	if IsNewPg(tb) {
+		require.NotEmpty(tb, reason, "reason must not be empty")
+
+		tb.Skipf("Skipping for new PostgreSQL handler: %s.", reason)
+	}
+}
+
 // IsPushdownDisabled returns true if FerretDB pushdowns are disabled.
 func IsPushdownDisabled() bool {
 	return *disableFilterPushdownF