diff --git a/01-messaging.md b/01-messaging.md
index 66232ab3c..8837357a7 100644
--- a/01-messaging.md
+++ b/01-messaging.md
@@ -318,6 +318,8 @@ For simplicity of diagnosis, it's often useful to tell a peer that something is
 
 #### Requirements
 
+The channel is referred to by `channel_id`, unless `channel_id` is 0 (i.e. all bytes are 0), in which case it refers to all channels.
+
 The funding node:
   - for all error messages sent before (and including) the `funding_created` message:
     - MUST use `temporary_channel_id` in lieu of `channel_id`.
@@ -330,7 +332,7 @@ A sending node:
   - SHOULD send `error` for protocol violations or internal errors that make channels unusable or that make further communication unusable.
   - SHOULD send `error` with the unknown `channel_id` in reply to messages of type `32`-`255` related to unknown channels.
   - when sending `error`:
-    - MUST fail the channel referred to by the error message.
+    - MUST fail the channel(s) referred to by the error message.
   - when sending `warning`:
 	- MAY set `channel_id` to all zero if the warning is not related to a specific channel.
   - MAY close the connection after sending.