diff --git a/xarray/core/variable.py b/xarray/core/variable.py
index 075d79043b2..8f4ff684b08 100644
--- a/xarray/core/variable.py
+++ b/xarray/core/variable.py
@@ -501,9 +501,6 @@ def __dask_postpersist__(self):
 
     @staticmethod
     def _dask_finalize(results, array_func, array_args, dims, attrs, encoding):
-        if isinstance(results, dict):  # persist case
-            name = array_args[0]
-            results = {k: v for k, v in results.items() if k[0] == name}
         data = array_func(results, *array_args)
         return Variable(dims, data, attrs=attrs, encoding=encoding)
 
diff --git a/xarray/tests/test_dask.py b/xarray/tests/test_dask.py
index 46685a29a47..489bf09fa3c 100644
--- a/xarray/tests/test_dask.py
+++ b/xarray/tests/test_dask.py
@@ -1607,3 +1607,10 @@ def test_more_transforms_pass_lazy_array_equiv(map_da, map_ds):
         assert_equal(map_da._from_temp_dataset(map_da._to_temp_dataset()), map_da)
         assert_equal(map_da.astype(map_da.dtype), map_da)
         assert_equal(map_da.transpose("y", "x", transpose_coords=False).cxy, map_da.cxy)
+
+
+def test_optimize():
+    a = dask.array.ones((10, 5), chunks=(1, 3))
+    arr = xr.DataArray(a).chunk(5)
+    (arr2,) = dask.optimize(arr)
+    arr2.compute()