If not repaired, a wobbly spindle problem will worsen and can become a hazard. (Spindles can eventually come undone, and allow a child or animal to slip through.)
Locate the wobbly spindle, and examine the area where it joins the staircase to determine where the extra space lies—you’ll find a small gap on one side. Most of the time, the problem area will be where the spindle connects beneath the stair rail, but it sometimes can be where the spindle meets the stair tread. Next, take a shim (above) and trim or break it at a size that approximates the gap. Then, apply wood glue to the narrow end of the shim and firmly force it into the space. Don’t worry about any excess.
Allow the glue to dry completely (follow manufacturer’s instructions). Then, use a box-cutter or utility knife to cut off the excess material as close to the rail as possible (right). Work slowly and carefully, so as not to mark up the spindle or the handrail. When you’re done, the shim will be securely in place, and so will the spindle.