diff --git a/funcy/seqs.py b/funcy/seqs.py
index 760a18e..d2e80fa 100644
--- a/funcy/seqs.py
+++ b/funcy/seqs.py
@@ -363,8 +363,12 @@ def _cut_iter(drop_tail, n, step, seq):
         if len(pool) < n:
             break
         yield pool
-        pool = pool[step:]
-        pool.extend(islice(it, step))
+        if step < n:
+            pool = pool[step:]
+            pool.extend(islice(it, step))
+        else:
+            take(step - n, it)  # discard the gap between parts
+            pool = take(n, it)
     if not drop_tail:
         for item in _cut_seq(drop_tail, n, step, pool):
             yield item
diff --git a/tests/test_seqs.py b/tests/test_seqs.py
index 4a4c0e6..d0c8534 100644
--- a/tests/test_seqs.py
+++ b/tests/test_seqs.py
@@ -170,6 +170,18 @@ def test_chunks():
     assert lchunks(2, 1, [0, 1, 2, 3]) == [[0, 1], [1, 2], [2, 3], [3]]
     assert lchunks(3, 1, iter(range(3))) == [[0, 1, 2], [1, 2], [2]]
 
+def test_partition_step_gt_n():
+    # The iterator path must skip step - n items between parts, like the
+    # Sequence path, when step > n.
+    assert lpartition(2, 3, iter(range(10))) == lpartition(2, 3, list(range(10)))
+    assert lpartition(2, 3, iter(range(10))) == [[0, 1], [3, 4], [6, 7]]
+
+def test_chunks_step_gt_n():
+    # The iterator path must skip step - n items between parts, like the
+    # Sequence path, when step > n.
+    assert lchunks(2, 3, iter(range(10))) == lchunks(2, 3, list(range(10)))
+    assert lchunks(2, 3, iter(range(10))) == [[0, 1], [3, 4], [6, 7], [9]]
+
 def test_partition_by():
     assert lpartition_by(lambda x: x == 3, [1,2,3,4,5]) == [[1,2], [3], [4,5]]
     assert lpartition_by('x', 'abxcd') == [['a', 'b'], ['x'], ['c', 'd']]