I wish the airlines would establish meaningful guidelines. CO (& UA) indicates "up to 14 in x 9 in x 22 in" along with "maximum combined linear measurement (L + W + H) of the carry-on bag is 45 inches". Since 14 + 9 + 22 = 45, and supposedly one is not to exceed a single one of those 3 dimensions, then the 45" max linear measurement constraint is redundant and misleading. I say misleading because it implies that there is flexibility with the individual dimensions so long as the sum <= 45 whereas the "up to" 14 x 9 x 22 constraint indicates that is not the case.

Other airlines, such as KL, are similar although the specific individual dimensions differ (e.g. KL's are 13.5" x 10" x 21.5"). If one were to satisfy both CO & KL (which is an upcoming itinerary of mine), then the max would be 13.5 x 9 x 21.5 (which add to 44).

I have traveled for years without incident -- domestically, to Canada, TATL & intra-Europe -- carrying on my trusty 22" Briggs & Riley (which is actually 14 x 9.75 x 22.5 including wheels & handles). Hopefully my luck will continue.

BTW, while I realize it is beyond the OP's budget, the B & R bags are truly excellent (I have 6) and the lifetime warranty has always been honored (for zippers, pulls, and one smushed-in corner). I highly recommend them.