I used 4-5 overcalls for a long time with a few regular partners... a variation we called 'Michelangelo', part Michaels and part Roman Jumps:
1C-2C = 4S 5+Red
1C-2D = 4H 5+D
1D-2D = 4M 5+C
1D-2H = 4S 5+H
1H-2H = 4S 5+m
We required 5-5 for 1S-2S and for 2NT showing minors since we were forced to the 3-level.
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What are you doing with 5/5s? Just bid them naturally? I'm hestitant to limit the amount you can make the two suited bit, having played these as 5/4 or better for a while now they are just so good when they come up that I want to maximise the frequency.
I am a big believer in having the 5-5s bid naturally, but allowing the artificial jumps to be 4-6 or 4-7. Part of their 'goodness' comes from partner knowing what to do at his turn, and he's going to assume 4-5.
Our simple overcalls DID still contain some 4-5 hands; 1C-2D was NF so had to be limited strength, with a strong 4-5 we started with 1D intending to reverse. With the cuebids you have room to fit in more than one strength range especially over the minors.
I was always a bit surprised, however, that Overcall Structure needed these: I used them in the context of simple overcalls promising 5 cards, such that 4-5s were easily lost after simple overcalls. If you allow a 1D overcall on 4-5 shape, and allow a 1M advance on 4, there is a bit less need for a 4-5 convention.
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What you gain is very limited compared to what you lose imo. I'd rather give up the natural 1NT and play Raptor than give up all of this to keep my natural 1NT overcall.
One reason I put two hand-shapes into the cuebid was so lost fewer of the weak jump shifts.
I would certainly be willing to consider giving up a natural 1NT overcall to handle more of the 4-5s (if you didn't have to specify both suits for it to be GCC) before I would be willing to give up three or more weak jumps.