diff --git a/src/osmium/replication/server.py b/src/osmium/replication/server.py
index 37f2e64..60ce965 100644
--- a/src/osmium/replication/server.py
+++ b/src/osmium/replication/server.py
@@ -65,6 +65,15 @@ def __init__(self, url: str, diff_type: str = 'osc.gz') -> None:
             than osc.gz files, set the `diff_type` to the given file suffix.
         """
 
+        # Canonicalize the baseurl to have exactle one trailing slash.
+        # Try to avoid calling `example.com/area-updates//state.txt`
+        # Don't turn `http://example.com/` into `http://example.com`
+        # Remove all trailing /'s then add one back
+        while url.endswith("/"):
+            url = url.rstrip("/")
+        # put a final / at the end
+        url = url + "/"
+
         self.baseurl = url
         self.diff_type = diff_type
         self.extra_request_params: Dict[str, Any] = dict(timeout=60, stream=True)
@@ -483,16 +492,19 @@ def get_state_url(self, seq: Optional[int]) -> str:
             i.e. the state file in the root directory of the replication
             service.
         """
+
+        # baseurl is guaranteed to end with /, as per __init__
         if seq is None:
-            return self.baseurl + '/state.txt'
+            return self.baseurl + 'state.txt'
 
-        return '%s/%03i/%03i/%03i.state.txt' % \
+        return '%s%03i/%03i/%03i.state.txt' % \
                (self.baseurl, seq / 1000000, (seq % 1000000) / 1000, seq % 1000)
 
     def get_diff_url(self, seq: int) -> str:
         """ Returns the URL to the diff file for the given sequence id.
         """
-        return '%s/%03i/%03i/%03i.%s' % \
+        # baseurl is guaranteed to end with /, as per __init__
+        return '%s%03i/%03i/%03i.%s' % \
                (self.baseurl,
                 seq / 1000000, (seq % 1000000) / 1000, seq % 1000,
                 self.diff_type)
diff --git a/test/test_replication.py b/test/test_replication.py
index bc5710d..5cc4246 100644
--- a/test/test_replication.py
+++ b/test/test_replication.py
@@ -22,28 +22,43 @@
 pytestmark = [pytest.mark.thread_unsafe, pytest.mark.iterations(1)]
 
 
-@pytest.mark.parametrize("inp,outp", [
-        (None,      'https://text.org/state.txt'),
-        (1,         'https://text.org/000/000/001.state.txt'),
-        (999,       'https://text.org/000/000/999.state.txt'),
-        (1000,      'https://text.org/000/001/000.state.txt'),
-        (573923,    'https://text.org/000/573/923.state.txt'),
-        (3290012,   'https://text.org/003/290/012.state.txt'),
+@pytest.mark.parametrize("baseurl,inp,outp", [
+        ("https://text.org",  None,      'https://text.org/state.txt'),
+        ("https://text.org",  1,         'https://text.org/000/000/001.state.txt'),
+        ("https://text.org",  999,       'https://text.org/000/000/999.state.txt'),
+        ("https://text.org",  1000,      'https://text.org/000/001/000.state.txt'),
+        ("https://text.org",  573923,    'https://text.org/000/573/923.state.txt'),
+        ("https://text.org",  3290012,   'https://text.org/003/290/012.state.txt'),
+
+        ("https://text.org/",  None,      'https://text.org/state.txt'),
+        ("https://text.org/",  1,         'https://text.org/000/000/001.state.txt'),
+        ("https://text.org//", None,      'https://text.org/state.txt'),
+        ("https://text.org//", 1,         'https://text.org/000/000/001.state.txt'),
+
+        ("https://text.org/area-updates",   None,    'https://text.org/area-updates/state.txt'),
+        ("https://text.org/area-updates",   3290012, 'https://text.org/area-updates/003/290/012.state.txt'),
+        ("https://text.org/area-updates/",  None,    'https://text.org/area-updates/state.txt'),
+        ("https://text.org/area-updates/",  3290012, 'https://text.org/area-updates/003/290/012.state.txt'),
+        ("https://text.org/area-updates//", None,    'https://text.org/area-updates/state.txt'),
+        ("https://text.org/area-updates//", 3290012, 'https://text.org/area-updates/003/290/012.state.txt'),
+        ("https://text.org/area-updates///", 3290012, 'https://text.org/area-updates/003/290/012.state.txt'),
     ])
-def test_get_state_url(inp, outp):
-    svr = rserv.ReplicationServer("https://text.org")
+def test_get_state_url(baseurl, inp, outp):
+    svr = rserv.ReplicationServer(baseurl)
 
     assert outp == svr.get_state_url(inp)
 
 
-@pytest.mark.parametrize("inp,outp", [
-        (1,         'https://who.is/me//000/000/001.osc.gz'),
-        (500,       'https://who.is/me//000/000/500.osc.gz'),
-        (83750,     'https://who.is/me//000/083/750.osc.gz'),
-        (999999999, 'https://who.is/me//999/999/999.osc.gz'),
+@pytest.mark.parametrize("baseurl,inp,outp", [
+        ("https://who.is/me/", 1,         'https://who.is/me//sdfsdf000/000/001.osc.gz'),
+        ("https://who.is/me/", 500,       'https://who.is/me/000/000/500.osc.gz'),
+        ("https://who.is/me/", 83750,     'https://who.is/me/000/083/750.osc.gz'),
+        ("https://who.is/me/", 999999999, 'https://who.is/me/999/999/999.osc.gz'),
+
+        ("https://who.is/me",  999999999, 'https://who.is/me/999/999/999.osc.gz'),
     ])
-def test_get_diff_url(inp, outp):
-    svr = rserv.ReplicationServer("https://who.is/me/")
+def test_get_diff_url(baseurl, inp, outp):
+    svr = rserv.ReplicationServer(baseurl)
 
     assert outp, svr.get_diff_url(inp)