"In Thoughts of You" was written by Geoff Morrow and Chris Arnold and was their first chart success. The two would write another hit for Fury with David Martin, "I'll Never Quite Get Over You". The B-side, "Away from You", was written by David Wilcox, David Elias and Keith Draper, who were members of the Liverpool beat group the Nocturns. Fury's manager Larry Parnes had bought some of the songs written by the three Nocturns members for "a small fee with a royalty clause built in" and one of the songs was decided to be the subsequent A-side single to "In Thoughts of You". However, Parnes and the three Norturns had a disagreement and the former pulled the plug on Fury recording any more of their songs after "Away from You".
