I'll offer an alternate fix that I find works very well (I have 3 Mighty Mice :)
Get a CLEAN sheet of paper. Put it on top of a stack of paper, i.e so you have a slightly soft cushioned surface, rather than directly on a hard desktop
Unplug your mouse (if USB) or switch it off (if Bluetooth).
Turn the mouse upside down and roll the scroll ball on the stack of paper, somewhat vigorously in circles, also back and forth and various directions. You will likely see some gunk come out of the scroll ball hole and stick to the paper. Don't roll over any of that loosened gunk. You may also see some stuff stuck to the ball itself, you can easily brush or blow that off.
The ball will heat up doing this, so don't do it for an extended period, or pause after several seconds to let it cool before trying again.
originally I used to always clean my first Mighty Mouse using the alcohol method, with limited success or requiring multiple cleaning attempts. Using this method, I find it works quickly and every time.
try it next time!