diff --git a/src/calibre/srv/library_broker.py b/src/calibre/srv/library_broker.py
index fe5c129045..def734a068 100644
--- a/src/calibre/srv/library_broker.py
+++ b/src/calibre/srv/library_broker.py
@@ -32,7 +32,12 @@ def samefile(a, b):
 def basename(path):
     while path and path[-1] in ('/' + os.sep):
         path = path[:-1]
-    return os.path.basename(path)
+    ans = os.path.basename(path)
+    if not ans:
+        # Can happen for a path like D:\ on windows
+        if len(path) == 2 and path[1] == ':':
+            ans = path[0]
+    return ans or 'Library'
 
 
 def init_library(library_path, is_default_library):
@@ -52,7 +57,7 @@ def make_library_id_unique(library_id, existing):
     return library_id
 
 
-def library_id_from_path(path, existing):
+def library_id_from_path(path, existing=frozenset()):
     library_id = basename(path).replace(' ', '_')
     return make_library_id_unique(library_id, existing)
 
diff --git a/src/calibre/srv/tests/routes.py b/src/calibre/srv/tests/routes.py
index 9b7bdf9210..36070bd353 100644
--- a/src/calibre/srv/tests/routes.py
+++ b/src/calibre/srv/tests/routes.py
@@ -6,11 +6,22 @@ from __future__ import (unicode_literals, division, absolute_import,
 __license__ = 'GPL v3'
 __copyright__ = '2015, Kovid Goyal <kovid at kovidgoyal.net>'
 
+import os
 from calibre.srv.tests.base import BaseTest
 
 
 class TestRouter(BaseTest):
 
+    def test_library_id_construction(self):
+        from calibre.srv.library_broker import library_id_from_path
+        self.ae(library_id_from_path('as'), 'as')
+        self.ae(library_id_from_path('as/'), 'as')
+        self.ae(library_id_from_path('as////'), 'as')
+        self.ae(library_id_from_path('/as/'), 'as')
+        if os.sep == '\\':
+            self.ae(library_id_from_path('as/' + os.sep), 'as')
+            self.ae(library_id_from_path('X:' + os.sep), 'X')
+
     def test_route_construction(self):
         ' Test route construction '
         from calibre.srv.routes import Route, endpoint, RouteError