In a 1984 Japanese television interview, Limahl said that Don't Suppose saw him experimenting much more than he did on White Feathers, Kajagoogoo's debut album (which included "Too Shy").

[citation needed] Much of the record features a string section; flutes and saxophones also join Limahl's keyboards.

[9] In France only, "The NeverEnding Story (L'histoire Sans Fin)", a French version of the song also sung by Limahl, was released as the B-side.

In March 2012, Gold Legion issued the album on CD in the US featuring remixes of "NeverEnding Story" and "Only for Love" as bonus tracks.

The first eight tracks were digitised by Dutch budget label Disky Communications for inclusion on the compilation album The Best of Limahl, released in 1996.

That album omits the last two tracks of Don't Suppose: "Tar Beach" and "Oh Girl"; also missing is "The Greenhouse Effect", although "The NeverEnding Story" is included.

In 2002, Disky released an abridged version of the compilation, Neverending Story: Best of Limahl, which included five songs from Don't Suppose.