How did Superman retain his secret identity when he constantly left Clark Kent's clothes behind? Even if they were shredded when he yanked them off in an emergency, they still would have been the same size, color and style of clothing his coworkers had just seen him wearing. Granted, when he wasn't in a hurry, he could use his super strength to compress them and then hide them, but I always pictured him tearing them off and leaving them in a heap. Lois: "Where's Clark?" Jimmy: "I don't know, but this looks like his suit. Hey! Look up in the sky!"
After the Superman movie with Christopher Reeves (in 1978), Elliot S. Magin wrote two books, Superman: Last Son of Krypton and Superman: Miracle Monday. The book format allowed time and space for some references and comments that would not always fit in a comic book, due to limited space. (Also, in my case, since comic books were banned in the house, I could read those books.)
In one of the books, Magin makes a reference to Superman folding his clothes up into tiny squares that he can easily keep in a pocket in his cape. This would also explain an unasked corollary to the above question: How come Superman can change back into the same suit he was previously wearing when he's not where he took off that suit?
He has a "pouch in his cape"
There is a reference in one of the Silver-Age Superman comics that specifically answers this question; This also goes some way to answering the question of why superman wears a cape.
In fairness to your question though, I've found several instances (in "Superman Returns" and "Lois and Clark) where he does simply abandon them but usually in circumstances where they're unlikely to be found such as in an elevator shaft or a disused factory: