I grew up speaking a variety of American English that merges the "short U" sounds before L. The "short U" sounds are the vowels in the words STRUT and FOOT. For me, before an L sound, all words have the vowel from FOOT—that is, for me bull, full, and pull rhyme with dull, gull, and null.
According to Wikipedia, The Atlas of North American English mentions this as one of four mergers before /l/ that may be under way in some accents of North American English, and which require more study. So this merger is known to exist, but it is not well understood the range and extent of the merger.
Regardless, I'd like to have a full grasp of standard American English, so I have set to the task of memorizing which -UL- words have the STRUT vowel (which I always pronounced with the FOOT vowel). Are there a set of rules I can use to predict if a "short U followed by L" word will have the STRUT vowel?