diff --git a/gunicorn/config.py b/gunicorn/config.py
index 99b4ba31..5549a372 100644
--- a/gunicorn/config.py
+++ b/gunicorn/config.py
@@ -495,11 +495,19 @@ def validate_chdir(val):
     return path
 
 
-def validate_address(val):
+def validate_statsd_address(val):
     val = validate_string(val)
     if val is None:
         return None
 
+    # As of major release 20, util.parse_address would recognize unix:PORT
+    # as a UDS address, breaking backwards compatibility. We defend against
+    # that regression here (this is also unit-tested).
+    # Feel free to remove in the next major release.
+    unix_hostname_regression = re.match(r'^unix:(\d+)$', val)
+    if unix_hostname_regression:
+        return ('unix', int(unix_hostname_regression.group(1)))
+
     try:
         address = util.parse_address(val, default_port='8125')
     except RuntimeError:
@@ -1473,7 +1481,7 @@ class StatsdHost(Setting):
     cli = ["--statsd-host"]
     meta = "STATSD_ADDR"
     default = None
-    validator = validate_address
+    validator = validate_statsd_address
     desc = """\
     The address of the StatsD server to log to.
 
diff --git a/tests/test_config.py b/tests/test_config.py
index db33cb3f..e3a3212b 100644
--- a/tests/test_config.py
+++ b/tests/test_config.py
@@ -313,12 +313,23 @@ def test_statsd_host():
     assert c.statsd_host == ("localhost", 8125)
     c.set("statsd_host", "statsd:7777")
     assert c.statsd_host == ("statsd", 7777)
-    c.set("statsd_host", "unix:/path/to.sock")
+    c.set("statsd_host", "unix:///path/to.sock")
     assert c.statsd_host == "/path/to.sock"
     pytest.raises(TypeError, c.set, "statsd_host", 666)
     pytest.raises(TypeError, c.set, "statsd_host", "host:string")
 
 
+def test_statsd_host_with_unix_as_hostname():
+    # This is a regression test for major release 20. After this release
+    # we should consider modifying the behavior of util.parse_address to
+    # simplify gunicorn's code
+    c = config.Config()
+    c.set("statsd_host", "unix:7777")
+    assert c.statsd_host == ("unix", 7777)
+    c.set("statsd_host", "unix://some.socket")
+    assert c.statsd_host == "some.socket"
+
+
 def test_statsd_changes_logger():
     c = config.Config()
     assert c.logger_class == glogging.Logger