Probably just a little hair from shaving, some soap and some toothpaste stuck in the trap. I've got a small plunger (12" handle) that I use about every four months and it cleans the trap very easily. Our sink has been in about two years.

Our stopper thingy doesn't come out either, some do and some you have to take the pipes apart.

The pop-up drain doesn't come out because it was installed with the arm (located underneath) inserted "through" the hole in the pop-up. Some work that way. Anyway, there should still be enough room to insert the "zip-it". Give it a try.

If that doesn't get a satisfactory result (eg. if it's not long enough to reach the clog), then put a small bucket under the p-trap, remove it, clean it out, and reinstall (checking for leaks).

Zip-its do exactly what the designer intend them to do,,,they extract $2 or $3 from your wallet. Any drain cleaning action they may achieve is strictly a bonus.

Put a bucket under the trap, then remove and clean the trap and you will most likely be done with the problem.

Our stopper gets gunked up occassionally and has to be removed and cleaned. You don't have to take the pipes apart to get it out. All you need to do is loosen the nut that connects the stopper arm to the tailpiece. You can them pull the arm out and your stopper will be free. If you reinstall the stopper with the tab facing to the side, the arm will not go through the stopper tab hole and you can pull it out without unhooking the arm. You may not get as tight a seal with the stopper this way.

Thanks, everyone! Your responses reminded me that I owned a small plunger intended for that purpose. It had gotten misplaced in the remodel, but you inspired me to look for it. (Ah, those unpacked boxed....)

Anyway, it did the job just fine. Which was great because I do not trust myself to take apart anything plumbing-related. Thanks again!