diff --git a/tests/rules/test_cd_correction.py b/tests/rules/test_cd_correction.py
new file mode 100644
index 0000000..d257658
--- /dev/null
+++ b/tests/rules/test_cd_correction.py
@@ -0,0 +1,23 @@
+import pytest
+from thefuck.rules.cd_correction import match
+from thefuck.types import Command
+
+
+@pytest.mark.parametrize('command', [
+    Command('cd foo', 'cd: foo: No such file or directory'),
+    Command('cd foo/bar/baz',
+            'cd: foo: No such file or directory'),
+    Command('cd foo/bar/baz', 'cd: can\'t cd to foo/bar/baz'),
+    Command('cd /foo/bar/', 'cd: The directory "/foo/bar/" does not exist')])
+def test_match(command):
+    assert match(command)
+
+
+@pytest.mark.parametrize('command', [
+    Command('cd foo', ''), Command('', '')])
+def test_not_match(command):
+    assert not match(command)
+
+
+# Note that get_new_command uses local filesystem, so not testing it here.
+# Instead, see the functional test `functional.test_cd_correction`
diff --git a/tests/rules/test_cd_mkdir.py b/tests/rules/test_cd_mkdir.py
index 61dc30e..aa3d82e 100644
--- a/tests/rules/test_cd_mkdir.py
+++ b/tests/rules/test_cd_mkdir.py
@@ -7,7 +7,8 @@ from thefuck.types import Command
     Command('cd foo', 'cd: foo: No such file or directory'),
     Command('cd foo/bar/baz',
             'cd: foo: No such file or directory'),
-    Command('cd foo/bar/baz', 'cd: can\'t cd to foo/bar/baz')])
+    Command('cd foo/bar/baz', 'cd: can\'t cd to foo/bar/baz'),
+    Command('cd /foo/bar/', 'cd: The directory "/foo/bar/" does not exist')])
 def test_match(command):
     assert match(command)
 
diff --git a/thefuck/rules/cd_correction.py b/thefuck/rules/cd_correction.py
index ca3464b..376e51e 100644
--- a/thefuck/rules/cd_correction.py
+++ b/thefuck/rules/cd_correction.py
@@ -21,9 +21,12 @@ def _get_sub_dirs(parent):
 @for_app('cd')
 def match(command):
     """Match function copied from cd_mkdir.py"""
-    return (command.script.startswith('cd ')
-            and ('no such file or directory' in command.output.lower()
-                 or 'cd: can\'t cd to' in command.output.lower()))
+    return (
+        command.script.startswith('cd ') and any((
+            'no such file or directory' in command.output.lower(),
+            'cd: can\'t cd to' in command.output.lower(),
+            'does not exist' in command.output.lower()
+        )))
 
 
 @sudo_support
@@ -37,7 +40,11 @@ def get_new_command(command):
     dest = command.script_parts[1].split(os.sep)
     if dest[-1] == '':
         dest = dest[:-1]
-    if six.PY2:
+
+    if dest[0] == '':
+        cwd = os.sep
+        dest = dest[1:]
+    elif six.PY2:
         cwd = os.getcwdu()
     else:
         cwd = os.getcwd()
diff --git a/thefuck/rules/cd_mkdir.py b/thefuck/rules/cd_mkdir.py
index 09e3ab6..363b92d 100644
--- a/thefuck/rules/cd_mkdir.py
+++ b/thefuck/rules/cd_mkdir.py
@@ -8,10 +8,11 @@ from thefuck.shells import shell
 @for_app('cd')
 def match(command):
     return (
-        'no such file or directory' in command.output.lower()
-        or 'cd: can\'t cd to' in command.output.lower()
-        or 'the system cannot find the path specified.' in command.output.lower()
-    )
+        command.script.startswith('cd ') and any((
+            'no such file or directory' in command.output.lower(),
+            'cd: can\'t cd to' in command.output.lower(),
+            'does not exist' in command.output.lower()
+        )))
 
 
 @sudo_support