According to Johnny Marr in his interview with Danny Kelly (NME 1991), he thinks the reason they signed to Rough Trade was because they had The Fall and The Monochrome Set - it's not clear whether Johnny is having trouble remembering, or if that's jujst why he suspects Morrissey wanted to sign to RT. I doubt it would have been solely down to Morrissey at the point anyway, and it's certainly true that both of them liked, respected and were influenced by The Fall (who, ironically, left soon after as they didn't want to be on a label where The Smiths were top priority).