diff --git a/svgpathtools/path.py b/svgpathtools/path.py
index ec23b71..7afd58e 100644
--- a/svgpathtools/path.py
+++ b/svgpathtools/path.py
@@ -2136,7 +2136,13 @@ class Path(MutableSequence):
 
     def cropped(self, T0, T1):
         """returns a cropped copy of the path."""
+        assert 0 <= T0 <= 1 and 0 <= T1<= 1
         assert T0 != T1
+        assert not (T0 == 1 and T1 == 0)
+
+        if T0 == 1 and 0 < T1 < 1 and self.isclosed():
+            return self.cropped(0, T1)
+
         if T1 == 1:
             seg1 = self[-1]
             t_seg1 = 1
@@ -2171,7 +2177,7 @@ class Path(MutableSequence):
 
             # T1<T0 must cross discontinuity case
             if T1 < T0:
-                if self.isclosed():
+                if not self.isclosed():
                     raise ValueError("This path is not closed, thus T0 must "
                                      "be less than T1.")
                 else:
diff --git a/test/test_path.py b/test/test_path.py
index 3d3cec3..e69499b 100644
--- a/test/test_path.py
+++ b/test/test_path.py
@@ -660,6 +660,35 @@ class TestPath(unittest.TestCase):
         self.assertTrue(chk1)
         self.assertTrue(chk2)
 
+    def test_cropped(self):
+        p_closed = Path(Line(0, 1), Line(1, 1 + 1j), Line(1 + 1j, 1j),
+                        Line(1j, 0))
+        first_half = Path(Line(0, 1), Line(1, 1 + 1j))
+        second_half = Path(Line(1 + 1j, 1j), Line(1j, 0))
+        middle_half = Path(Line(1, 1 + 1j), Line(1 + 1j, 1j))
+        other_middle_half = Path(Line(1j, 0), Line(0, 1))
+        self.assertTrue(p_closed.cropped(0, 0.5) == first_half)
+        self.assertTrue(p_closed.cropped(1, 0.5) == first_half)
+        self.assertTrue(p_closed.cropped(.5, 1) == second_half)
+        self.assertTrue(p_closed.cropped(0.25, 0.75) == middle_half)
+        self.assertTrue(p_closed.cropped(0.75, 0.25) == other_middle_half)
+        with self.assertRaises(AssertionError):
+            p_closed.cropped(1, 0)
+        with self.assertRaises(AssertionError):
+            p_closed.cropped(.5, 1.1)
+        with self.assertRaises(AssertionError):
+            p_closed.cropped(-0.1, 0.1)
+
+        p_open = Path(Line(0, 1), Line(1, 1 + 1j), Line(1 + 1j, 1j),
+                      Line(1j, 2j))
+        self.assertTrue(p_open.cropped(0, 0.5) == first_half)
+        with self.assertRaises(ValueError):
+            p_open.cropped(.75, .25)
+        with self.assertRaises(ValueError):
+            p_open.cropped(1, .25)
+        with self.assertRaises(AssertionError):
+            p_open.cropped(1, 0)
+
 
 class Test_ilength(unittest.TestCase):
     # See svgpathtools.notes.inv_arclength.py for information on how these