diff --git a/semver.py b/semver.py
index d82718b..4d1c6eb 100644
--- a/semver.py
+++ b/semver.py
@@ -146,13 +146,29 @@ def compare(ver1, ver2):
     """
     def nat_cmp(a, b):
         def convert(text):
-            return (2, int(text)) if re.match('[0-9]+', text) else (1, text)
+            return int(text) if re.match('[0-9]+', text) else text
 
         def split_key(key):
             return [convert(c) for c in key.split('.')]
 
+        def cmp_prerelease_tag(a, b):
+            if isinstance(a, int) and isinstance(b, int):
+                return cmp(a, b)
+            elif isinstance(a, int):
+                return -1
+            elif isinstance(b, int):
+                return 1
+            else:
+                return cmp(a, b)
+
         a, b = a or '', b or ''
-        return cmp(split_key(a), split_key(b))
+        a_parts, b_parts = split_key(a), split_key(b)
+        for sub_a, sub_b in zip(a_parts, b_parts):
+            cmp_result = cmp_prerelease_tag(sub_a, sub_b)
+            if cmp_result != 0:
+                return cmp_result
+        else:
+            return cmp(len(a), len(b))
 
     def compare_by_keys(d1, d2):
         for key in ['major', 'minor', 'patch']:
diff --git a/tests.py b/tests.py
index 5681aef..1e724ef 100644
--- a/tests.py
+++ b/tests.py
@@ -70,10 +70,24 @@ def test_should_parse_zero_prerelease():
 
 def test_should_get_less():
     assert compare("1.0.0", "2.0.0") == -1
+    assert compare('1.0.0-alpha', '1.0.0-alpha.1') == -1
+    assert compare('1.0.0-alpha.1', '1.0.0-alpha.beta') == -1
+    assert compare('1.0.0-alpha.beta', '1.0.0-beta') == -1
+    assert compare('1.0.0-beta', '1.0.0-beta.2') == -1
+    assert compare('1.0.0-beta.2', '1.0.0-beta.11') == -1
+    assert compare('1.0.0-beta.11', '1.0.0-rc.1') == -1
+    assert compare('1.0.0-rc.1', '1.0.0') == -1
 
 
 def test_should_get_greater():
     assert compare("2.0.0", "1.0.0") == 1
+    assert compare('1.0.0-alpha.1', '1.0.0-alpha') == 1
+    assert compare('1.0.0-alpha.beta', '1.0.0-alpha.1') == 1
+    assert compare('1.0.0-beta', '1.0.0-alpha.beta') == 1
+    assert compare('1.0.0-beta.2', '1.0.0-beta') == 1
+    assert compare('1.0.0-beta.11', '1.0.0-beta.2') == 1
+    assert compare('1.0.0-rc.1', '1.0.0-beta.11') == 1
+    assert compare('1.0.0', '1.0.0-rc.1') == 1
 
 
 def test_should_match_simple():
@@ -232,7 +246,7 @@ def test_prerelease_order():
     assert min_ver('1.2.3-Rc10', '1.2.3-rc10') == '1.2.3-Rc10'
     # Numeric identifiers always have lower precedence than non-numeric
     # identifiers.
-    assert min_ver('1.2.3-2', '1.2.3-rc') == '1.2.3-rc'
+    assert min_ver('1.2.3-2', '1.2.3-rc') == '1.2.3-2'
     # A larger set of pre-release fields has a higher precedence than a
     # smaller set, if all of the preceding identifiers are equal.
     assert min_ver('1.2.3-rc.2.1', '1.2.3-rc.2') == '1.2.3-rc.2'