diff --git a/api/client-server/v1/rooms.yaml b/api/client-server/v1/rooms.yaml
index 1cce76f3..ff5587a9 100644
--- a/api/client-server/v1/rooms.yaml
+++ b/api/client-server/v1/rooms.yaml
@@ -312,9 +312,9 @@ paths:
                   }
                 ],
                 "visibility": "private",
-                "private_user_data": [{
+                "account_data": [{
                     "type": "m.tag",
-                    "content": {"tags": {"work": {"order": 1}}}
+                    "content": {"tags": {"work": {"order": "1"}}}
                 }]
               }
           schema:
@@ -375,7 +375,7 @@ paths:
                 description: |-
                   Whether this room is visible to the ``/publicRooms`` API
                   or not."
-              private_user_data:
+              account_data:
                 type: array
                 description: |-
                   The private data that this user has attached to this room.
diff --git a/api/client-server/v1/sync.yaml b/api/client-server/v1/sync.yaml
index 57a15583..b8608171 100644
--- a/api/client-server/v1/sync.yaml
+++ b/api/client-server/v1/sync.yaml
@@ -254,7 +254,7 @@ paths:
                               }
                           ],
                           "visibility": "private",
-                          "private_user_data": [
+                          "account_data": [
                             {
                               "type": "m.tag",
                               "content": {"tags": {"work": {"order": 1}}}
@@ -352,7 +352,7 @@ paths:
                       description: |-
                         Whether this room is visible to the ``/publicRooms`` API
                         or not."
-                    private_user_data:
+                    account_data:
                       type: array
                       description: |-
                         The private data that this user has attached to
diff --git a/api/client-server/v2_alpha/sync.yaml b/api/client-server/v2_alpha/sync.yaml
index f8d5a2a9..e2016d68 100644
--- a/api/client-server/v2_alpha/sync.yaml
+++ b/api/client-server/v2_alpha/sync.yaml
@@ -139,7 +139,7 @@ paths:
                             e.g. typing.
                           allOf:
                             - $ref: "definitions/event_batch.json"
-                        private_user_data:
+                        account_data:
                           title: Private User Data
                           type: object
                           description: |-
@@ -297,7 +297,7 @@ paths:
                           }
                         ]
                       },
-                      "private_user_data": {
+                      "account_data": {
                         "events": [
                           {
                             "type": "m.tags",
diff --git a/api/client-server/v2_alpha/tags.yaml b/api/client-server/v2_alpha/tags.yaml
index 009e6000..91945dca 100644
--- a/api/client-server/v2_alpha/tags.yaml
+++ b/api/client-server/v2_alpha/tags.yaml
@@ -55,7 +55,7 @@ paths:
             application/json: |-
               {
                 "tags": {
-                  "work": {"order": 1},
+                  "work": {"order": "1"},
                   "pinned": {}
                 }
               }
@@ -97,7 +97,7 @@ paths:
           schema:
             type: object
             example: |-
-              {"order": 1}
+              {"order": "1"}
       responses:
         200:
           description:
diff --git a/specification/modules/tags.rst b/specification/modules/tags.rst
index 3d45975c..bb467bc0 100644
--- a/specification/modules/tags.rst
+++ b/specification/modules/tags.rst
@@ -11,16 +11,35 @@ Events
 ------
 
 The tags on a room are received as single ``m.tag`` event in the
-``private_user_data`` section of a room in a v2 /sync.
+``account_data`` section of a room in a v2 /sync.
 
 The ``m.tag`` can also be received in a v1 /events response or in the
-``private_user_data`` section of a room in v1 /initialSync. ``m.tag``
+``account_data`` section of a room in v1 /initialSync. ``m.tag``
 events appearing in v1 /events will have a ``room_id`` with the room
 the tags are for.
 
 Each tag has an associated JSON object with information about the tag, e.g how
 to order the rooms with a given tag.
 
+Ordering information is given under the ``order`` key as a string. The string
+are compared lexicographically by unicode codepoint to determine which should
+displayed first. So a room with a tag with an ``order`` key of ``"apples"``
+would appear before a room with a tag with an ``order`` key of ``"oranges"``.
+If a room has a tag without an ``order`` key then it should appear after the
+rooms with that tag that have an ``order`` key.
+
+The name of a tag MUST not exceed 255 bytes.
+
+The name of a tag should be human readable. When displaying tags for a room a
+client should display this human readable name. When adding a tag for a room
+a client may offer a list to choose from that includes all the tags that the
+user has previously set on any of their rooms.
+
+Two special names are listed in the specification:
+
+* ``m.favourite``
+* ``m.lowpriority``
+
 {{m_tag_event}}
 
 Client Behaviour