I can't really answer how "little power" I'd be willing to carry in a handgun, as "power" is generally most easily connected to "muzzle energy" ...
Using simple muzzle energy calculations to predict handgun bullet weight or caliber effectiveness in immediately incapacitating a person, or an animal, is at best arguably problematic ...
You can browse among the archived threads for topics related to this subject over on the Tactical Forums, under the Terminal Effects Section, and find quite a bit of information ... much of it offered by medical professionals, and/or referenced from medical journals and articles dealing with the trauma caused by the effects of bullet wounds on human bodies. It's not a "chit chat" forum, but you can quietly search out and read quite a bit of information not commonly found in some other forums.
Link to main page of Tactical Forums:
http://64.177.53.248/cgi-bin/tacticalubb/Ultimate.cgi?action=intro&BypassCookie=true
The "least" caliber in a handgun I'd personally consider lawfully carrying for defensive use is a .38 J-frame S&W revolver. That wasn't always the case, though, and as a young cop I remember carrying various handguns chambered in .22LR, .25 ACP and .380 ACP. A few more years in L/E pretty much convinced me that the "convenience" gained by being able to pocket a "minor caliber" pocket pistol might not turn out to be so "convenient" if I really NEEDED a defensive handgun, after all ....
Nowadays, whenever I find myself attracted by some shiny new example of one of the ever-growing number of watch-fob sized handguns, I stop and ask myself if I'd feel confident trying to stop an enraged and attacking pit bull with it. I decided to draw the line at .38 Special, and prefer either all-lead, or jacketed/bonded, +P hollowpoints, even then.
Regarding some of the spin-off thoughts within this thread ...
I have no idea what "enough gun" might be ...
If I reasonably suspected I was about to be involved in a gunfight during the course of my job that I couldn't avoid, I don't think the terms "enough gun" and "handgun" would even come close to appearing within the same sentence. Under those conditions, "Enough handgun" might even be my very favorite oxymoron of the moment.
I'd reach for a shotgun or a rifle ... and still wish I could be anywhere else but there.
Where the hell is Air Wolf when you need it, anyway????
Actually, I seem to remember calling for cover one time, when things were getting a bit fuzzy ... and in a moment of frustration I said something under my breath to the effect that they should also send Air Wolf ... while my mike was still activated. Naturally, while some of the responding units only heard some of the details being broadcast, everyone appeared to hear my muttered request for Air Wolf's response. Talk about selective listening ....