diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 4def2e4b93553..b209a6556709b 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -705,6 +705,10 @@ def _difference(self, other, sort=None):
             else:
                 return super()._difference(other, sort=sort)
 
+        elif len(overlap) == 2 and overlap[0] == first[0] and overlap[-1] == first[-1]:
+            # e.g. range(-8, 20, 7) and range(13, -9, -3)
+            return self[1:-1]
+
         if overlap.step == first.step:
             if overlap[0] == first.start:
                 # The difference is everything after the intersection
@@ -712,6 +716,10 @@ def _difference(self, other, sort=None):
             elif overlap[-1] == first[-1]:
                 # The difference is everything before the intersection
                 new_rng = range(first.start, overlap[0], first.step)
+            elif overlap._range == first[1:-1]:
+                # e.g. range(4) and range(1, 3)
+                step = len(first) - 1
+                new_rng = first[::step]
             else:
                 # The difference is not range-like
                 # e.g. range(1, 10, 1) and range(3, 7, 1)
@@ -725,16 +733,19 @@ def _difference(self, other, sort=None):
             if overlap.step == first.step * 2:
                 if overlap[0] == first[0] and overlap[-1] in (first[-1], first[-2]):
                     # e.g. range(1, 10, 1) and range(1, 10, 2)
-                    return self[1::2]
+                    new_rng = first[1::2]
 
                 elif overlap[0] == first[1] and overlap[-1] in (first[-1], first[-2]):
                     # e.g. range(1, 10, 1) and range(2, 10, 2)
-                    return self[::2]
+                    new_rng = first[::2]
 
-                # We can get here with  e.g. range(20) and range(0, 10, 2)
+                else:
+                    # We can get here with  e.g. range(20) and range(0, 10, 2)
+                    return super()._difference(other, sort=sort)
 
-            # e.g. range(10) and range(0, 10, 3)
-            return super()._difference(other, sort=sort)
+            else:
+                # e.g. range(10) and range(0, 10, 3)
+                return super()._difference(other, sort=sort)
 
         new_index = type(self)._simple_new(new_rng, name=res_name)
         if first is not self._range:
diff --git a/pandas/tests/indexes/ranges/test_setops.py b/pandas/tests/indexes/ranges/test_setops.py
index 583391bd96a85..2942010af2720 100644
--- a/pandas/tests/indexes/ranges/test_setops.py
+++ b/pandas/tests/indexes/ranges/test_setops.py
@@ -377,6 +377,24 @@ def test_difference_mismatched_step(self):
         result = obj[::-1].difference(obj[1::2], sort=False)
         tm.assert_index_equal(result, expected[::-1], exact=True)
 
+    def test_difference_interior_overlap_endpoints_preserved(self):
+        left = RangeIndex(range(4))
+        right = RangeIndex(range(1, 3))
+
+        result = left.difference(right)
+        expected = RangeIndex(0, 4, 3)
+        assert expected.tolist() == [0, 3]
+        tm.assert_index_equal(result, expected, exact=True)
+
+    def test_difference_endpoints_overlap_interior_preserved(self):
+        left = RangeIndex(-8, 20, 7)
+        right = RangeIndex(13, -9, -3)
+
+        result = left.difference(right)
+        expected = RangeIndex(-1, 13, 7)
+        assert expected.tolist() == [-1, 6]
+        tm.assert_index_equal(result, expected, exact=True)
+
     def test_difference_interior_non_preserving(self):
         # case with intersection of length 1 but RangeIndex is not preserved
         idx = Index(range(10))