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I have several pocket pistols. I've carried the P3At and a LCP.
I'd suggest the P238. It's a mini-1911, actually a Colt design that Sig bought. I also like the safety, which you can engage with the hammer down.
I'll 2nd the NAA. A Black widow in .22 mag is significantly smaller than any of the pocket autos. While the round is a bit weaker, the flash and report is something to behold. Anyone on the other end of that, at close range, is going to be deaf and blind for a few seconds at least.
The next thing up is a P32 Keltec, which is also worth considering. It is the smallest auto, period. It's enough smaller than the P3AT that I can hide it in places the .380 won't go, such as a manicure case.