There are a few things you can do. Make sure the height adjust springs are firm enough to hold the weight of the pickup in the mounting ring. If the pickup is adjusted low the compression spring become looser and can cause the pickup to vibrate or move more freely. I would use a soft foam rubber often found as packing material in pickup boxes and cut a small portion and place it into the cavity of the loose pickup. If the springs are weak, you can find after market springs that will most likely do the job. Make sure the pickup is the right size for the mounting ring. With all the modern after market accessories, this could be a problem. We are finding many American Standards mixed with Metric parts and it can cause problems trying to find parts that work together.