Sorry, I should have specified that specifically it was 3-3-4-3 and shown (no we don't lose that).
Next in this sequence having shown 1 control only for the limited HCP we denial cue AKQ (different rules for different strengths and shapes having spent some time with this over the last 2 decades!!).
eg if having shown 0-4/5 step 1=0 Q , 2=Q, 3=K, 4=QQ/A, 5=KQ
5-9 step 1= no control, 2= K, 3= A, 4=KK, 5=AK, 6=KKK
8+ positive starts with base =2 (but if signoff without control ask, not only does responder require additional values but step1=base of 3, and if "signedoff having show extras but not quantified controls, base=5)
opening bid assumes base =3
As to your complaints about "multi-cues" ie A/K/short, that is a matter for the partnership to institute its own rules firstly as to when multicues apply and secondly as to how to apply them.
My personal rules with partners include:-
a) hand defines shape first if possible to show length of side suits

if raising partner's suit on limited basis define your terms (eg HCP, cover cards, limit, forcing, slam-try)
c) where one hand knows the other hand's cover card number, the issue is as to specific cards : so usually A before K (with NT for trumps)
d) where the "numbers" are indeterminate (eg following Strong Club/FP opening and intervention then suit agreement) multi cues are appropriate but now
i) on the first opportunity to show a control in a suit you do NOT show distributional controls (shortage) in partner's known long suit
ii) higher NT is needed for DI
iii) once you embark on this route you do NOT stick Bw/KCB etc into the middle of the auction: you went this way for a reason and you continue...whichever form of cue-bidding has been commenced.
In contrast to most, I will use some form of Bw very very rarely: preferring to bid the slam direct or cue-bid: the only time I use KCB (or Kickback in more sophisticated partnerships) is simply to check that I have the requisite numbers as the prior auction should have indicated the strength ....
All bidding is a compromise, but as a classical music lover and Hifi nut (but with a wife who precludes ridiculous expenditure on it) I still HATE MP3 for serious music: that is one compormise I won't make!
regards