I decided to tighten up the axis bolts, as Stacey did above. I found that each of the two bolts on the RA axis were loose. In case anyone else is thinking of checking, here is a quick overview of the process (with photos).
1. Remove the four bolts connecting the black metal motor cover.
2. This exposes the motor which remains surrounded by a metal protective enclosure. This enclosure also has to be removed. (As Roland has explained elsewhere, the four bolts here are shorter than those in step #1. Do not mix them up and make sure each set of four is put back in its correct place.) The two bolts that need to be tightened were behind the bottom part of this enclosure.
3. This exposes the two bolts that needed tightening. Here is an image of one of them, at the bottom center of the image.
Once this bolt and the one on the other side were tightened, any looseness in the axis went away.