diff --git a/pyopencl/algorithm.py b/pyopencl/algorithm.py
index 40c6a81467afc372ab49b29d97348c18392a13d3..302c0a7901932768a1cc2b8242a2138b69856ea7 100644
--- a/pyopencl/algorithm.py
+++ b/pyopencl/algorithm.py
@@ -1026,7 +1026,17 @@ class ListOfListsBuilder:
 
               This implies that all lists are contiguous.
 
-              *event* is a :class:`pyopencl.Event` for dependency management.
+            If eliminate_empty_output_lists is set to True, *lists* has two
+            additional attributes ``num_nonempty_lists`` and ``indices``
+
+            * ``num_nonempty_lists`` for the number of nonempty lists.
+            * ``indices`` for the index of nonempty list in input objects.
+
+            In this case, `starts` has `num_nonempty_lists` + 1 entries. The *i*'s
+            entry is the start of the *i*'th nonempty list, which is generated by
+            the object with index *indices[i]*.
+
+            *event* is a :class:`pyopencl.Event` for dependency management.
 
         .. versionchanged:: 2016.2
 
@@ -1096,9 +1106,12 @@ class ListOfListsBuilder:
                 **dict(wait_for=wait_for))
 
         if self.eliminate_empty_output_lists:
+            compress_events = {}
             for name, dtype in self.list_names_and_dtypes:
                 if name in omit_lists:
                     continue
+                if name in self.count_sharing:
+                    continue
 
                 info_record = result[name]
                 info_record.indices = cl.array.empty(
@@ -1108,7 +1121,7 @@ class ListOfListsBuilder:
                 info_record.mask_scan = cl.array.empty(
                     queue, (n_objects + 1,), index_dtype, allocator=allocator)
                 info_record.mask_scan[0] = 0
-                info_record.compress_events = compress_kernel(
+                compress_events[name] = compress_kernel(
                     info_record.starts,
                     info_record.indices,
                     info_record.mask_scan,
@@ -1127,7 +1140,7 @@ class ListOfListsBuilder:
 
             info_record = result[name]
             if self.eliminate_empty_output_lists:
-                info_record.compress_events.wait()
+                compress_events[name].wait()
                 num_nonempty_lists = info_record.num_nonempty_lists.get()[0]
                 info_record.num_nonempty_lists = num_nonempty_lists
                 info_record.starts = info_record.starts[:num_nonempty_lists + 1]