Let me start with:
"It's a free country, all'yall can shoot whatever you want in a snub nose .38"
With that said however, let's consider a few things:
1) The standard pressure .38 Special is considered my many to be the "floor" for self defense (along with the 9mm in a semiautomatic). However that assumption is based on the performance of a .38 Special in a 4" service revolver.
2) Out of a 2" snub nose revolver, you're going to lose between 75 fps and 100 fps in velocity with a standard pressure .38 depending on the specific load. In field use, that's enough to put the standard pressure .38 Special from a 2" revolver in the same class as a .380 ACP out of a 3.5"-4" barrel.
There is a great deal of irony to be found when you encounter someone who's a fan of the standard pressure .38 in a snub nose revolver with 5 rounds, but who looks down his nose at someone carrying a PP in .380 ACP with 8 rounds in the pistol.
3) .38 +P loads lose even more velocity going from a 4" barrel to a 2" barrel, but they start out a lot faster. So even though they'll lose about 150 fps relative to a 4" service revolver, you'll still get velocities in the 900fps-950 fps range with 158gr and 125gr bullets respectively.
4) With a decently designed grip .38 +P loads are still quite manageable even in an lightweight revolver, so my advice is if you're going to use a 2" lightweight revolver for self defense, use a +P load. Don't kid yourself that 2" standard pressure results will be the same as 4" standard pressure results.
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Personally, I've never seen the advantage of the lightweight J-frame revolvers. The all steel Model 36 and Model 60 revolvers are much more durable, allowing you to practice regularly with a substantial number of rounds without wearing them out or loosening them up, they are easier to shoot accurately and rapidly due to the extra 6-7 ounces, but that extra weight does not prevent you from carrying one IWB all day long in comfort.