It appears on the compilation albums The World Won't Listen and Louder Than Bombs, and on the deluxe edition of The Queen Is Dead in 2017.
This song was only performed live once on 1 October 1985, at Eden Court in Inverness, on the final day of their 1985 Scotland tour.
[1] The original 12-inch and CD singles have "Rubber Ring" and "Asleep" segued into a continuous piece with the voice sample at the end of the former looped and faded into the wind noise preceding the latter.
Described by Simon Goddard (in Songs That Saved Your Life, 2nd edition, p. 154) as a "spectacular combination" — a suggestion with which Johnny Marr concurs — this carefully executed sequence could only be found on the original 12-inch and CD singles, before the 2017 release of the remaster/re-issue of The Queen Is Dead, which includes the same songs with the same segue as tracks 10 and 11 (respectively) of its "Additional Recordings" bonus disc.
Jack Rabid of Allmusic describes "Asleep" as "lullaby-ish", and the entire single as "great ... just another feather in a jeweled cap".