diff --git a/pyicloud/base.py b/pyicloud/base.py
index 87fa533..da1246a 100644
--- a/pyicloud/base.py
+++ b/pyicloud/base.py
@@ -114,7 +114,7 @@ class PyiCloudSession(requests.Session):
     def _raise_error(self, code, reason):
         if self.service.requires_2sa and \
                 reason == 'Missing X-APPLE-WEBAUTH-TOKEN cookie':
-            raise PyiCloud2SARequiredError(response.url)
+            raise PyiCloud2SARequiredError(self.service.user['apple_id'])
         if code == 'ZONE_NOT_FOUND' or code == 'AUTHENTICATION_FAILED':
             reason = 'Please log into https://icloud.com/ to manually ' \
                 'finish setting up your iCloud service'
diff --git a/pyicloud/exceptions.py b/pyicloud/exceptions.py
index f3cadea..8a65a54 100644
--- a/pyicloud/exceptions.py
+++ b/pyicloud/exceptions.py
@@ -25,8 +25,8 @@ class PyiCloudFailedLoginException(PyiCloudException):
 
 
 class PyiCloud2SARequiredError(PyiCloudException):
-    def __init__(self, url):
-        message = "Two-step authentication required for %s" % url
+    def __init__(self, apple_id):
+        message = "Two-step authentication required for account: %s" % apple_id
         super(PyiCloud2SARequiredError, self).__init__(message)