First off you should make sure that you aren't going too long between removals. If I go more than 4 days I have a huge mess on my hands. 4 days is the magic number for me.

Also, use just a little bit of adhesive remover. Don't use too much. Put it on your fingers and rub it into the lace a few minutes before doing a mirror slide.

And in my opinion, the magazine slide is inferior for removing glue. Use the mirror slide and get some tacky pallet stretch wrap to remove whatever the mirror doesn't get.

Oh yea, and BTW.....this is for preventative maintenance. If you keep it clean you really shouldn't get buildup, but if you do you might have to soak the piece or use something that can pressurize and spray your alcohol or remover, like a fabric gun or a waterpik, (but you gotta be careful with these)