diff --git a/pkg/local_object_storage/engine/delete_test.go b/pkg/local_object_storage/engine/delete_test.go
index 53c62981cd..bbc27615ae 100644
--- a/pkg/local_object_storage/engine/delete_test.go
+++ b/pkg/local_object_storage/engine/delete_test.go
@@ -18,6 +18,8 @@ import (
 )
 
 func TestDeleteBigObject(t *testing.T) {
+	t.Parallel()
+
 	defer os.RemoveAll(t.Name())
 
 	cnr := cidtest.ID()
diff --git a/pkg/local_object_storage/engine/evacuate_test.go b/pkg/local_object_storage/engine/evacuate_test.go
index bea6d4ff59..bc5b05ef0f 100644
--- a/pkg/local_object_storage/engine/evacuate_test.go
+++ b/pkg/local_object_storage/engine/evacuate_test.go
@@ -77,6 +77,8 @@ func newEngineEvacuate(t *testing.T, shardNum int, objPerShard int) (*StorageEng
 }
 
 func TestEvacuateShard(t *testing.T) {
+	t.Parallel()
+
 	const objPerShard = 3
 
 	e, ids, objects := newEngineEvacuate(t, 3, objPerShard)
@@ -132,6 +134,8 @@ func TestEvacuateShard(t *testing.T) {
 }
 
 func TestEvacuateNetwork(t *testing.T) {
+	t.Parallel()
+
 	var errReplication = errors.New("handler error")
 
 	acceptOneOf := func(objects []*objectSDK.Object, max int) func(context.Context, oid.Address, *objectSDK.Object) error {
@@ -154,6 +158,7 @@ func TestEvacuateNetwork(t *testing.T) {
 	}
 
 	t.Run("single shard", func(t *testing.T) {
+		t.Parallel()
 		e, ids, objects := newEngineEvacuate(t, 1, 3)
 		evacuateShardID := ids[0].String()
 
@@ -173,6 +178,7 @@ func TestEvacuateNetwork(t *testing.T) {
 		require.Equal(t, 2, res.Count())
 	})
 	t.Run("multiple shards, evacuate one", func(t *testing.T) {
+		t.Parallel()
 		e, ids, objects := newEngineEvacuate(t, 2, 3)
 
 		require.NoError(t, e.shards[ids[0].String()].SetMode(mode.ReadOnly))
@@ -195,6 +201,7 @@ func TestEvacuateNetwork(t *testing.T) {
 		})
 	})
 	t.Run("multiple shards, evacuate many", func(t *testing.T) {
+		t.Parallel()
 		e, ids, objects := newEngineEvacuate(t, 4, 5)
 		evacuateIDs := ids[0:3]
 
@@ -229,6 +236,7 @@ func TestEvacuateNetwork(t *testing.T) {
 }
 
 func TestEvacuateCancellation(t *testing.T) {
+	t.Parallel()
 	e, ids, _ := newEngineEvacuate(t, 2, 3)
 
 	require.NoError(t, e.shards[ids[0].String()].SetMode(mode.ReadOnly))
diff --git a/pkg/local_object_storage/engine/list_test.go b/pkg/local_object_storage/engine/list_test.go
index 44062be686..5b927cf11b 100644
--- a/pkg/local_object_storage/engine/list_test.go
+++ b/pkg/local_object_storage/engine/list_test.go
@@ -29,6 +29,8 @@ func sortAddresses(addrWithType []object.AddressWithType) []object.AddressWithTy
 }
 
 func TestListWithCursor(t *testing.T) {
+	t.Parallel()
+
 	tests := []struct {
 		name      string
 		shardNum  int
@@ -60,8 +62,10 @@ func TestListWithCursor(t *testing.T) {
 			batchSize: 100,
 		},
 	}
-	for _, tt := range tests {
+	for i := range tests {
+		tt := tests[i]
 		t.Run(tt.name, func(t *testing.T) {
+			t.Parallel()
 			e := testNewEngine(t).setShardsNumOpts(t, tt.shardNum, func(id int) []shard.Option {
 				return []shard.Option{
 					shard.WithLogger(&logger.Logger{Logger: zap.L()}),
diff --git a/pkg/local_object_storage/engine/lock_test.go b/pkg/local_object_storage/engine/lock_test.go
index 4c89b92265..7796913ea6 100644
--- a/pkg/local_object_storage/engine/lock_test.go
+++ b/pkg/local_object_storage/engine/lock_test.go
@@ -31,6 +31,8 @@ func (t tss) IsTombstoneAvailable(ctx context.Context, _ oid.Address, epoch uint
 }
 
 func TestLockUserScenario(t *testing.T) {
+	t.Parallel()
+
 	// Tested user actions:
 	//   1. stores some object
 	//   2. locks the object
@@ -146,6 +148,8 @@ func TestLockUserScenario(t *testing.T) {
 }
 
 func TestLockExpiration(t *testing.T) {
+	t.Parallel()
+
 	// Tested scenario:
 	//   1. some object is stored
 	//   2. lock object for it is stored, and the object is locked
@@ -222,6 +226,8 @@ func TestLockExpiration(t *testing.T) {
 }
 
 func TestLockForceRemoval(t *testing.T) {
+	t.Parallel()
+
 	// Tested scenario:
 	//   1. some object is stored
 	//   2. lock object for it is stored, and the object is locked
diff --git a/pkg/local_object_storage/engine/remove_copies_test.go b/pkg/local_object_storage/engine/remove_copies_test.go
index c53e03bbf2..8131fcf0d5 100644
--- a/pkg/local_object_storage/engine/remove_copies_test.go
+++ b/pkg/local_object_storage/engine/remove_copies_test.go
@@ -17,6 +17,8 @@ import (
 )
 
 func TestRebalance(t *testing.T) {
+	t.Parallel()
+
 	te := newEngineWithErrorThreshold(t, "", 0)
 
 	const (
@@ -101,6 +103,8 @@ loop:
 }
 
 func TestRebalanceSingleThread(t *testing.T) {
+	t.Parallel()
+
 	te := newEngineWithErrorThreshold(t, "", 0)
 
 	obj := testutil.GenerateObjectWithCID(cidtest.ID())