With few exceptions, the vast majority of .38 Sp JHP's fail to expand when fired from 2" barrels in the 4 layer denim test. Many of the lighter JHP's demonstrate overexpansion and insufficient penetration in bare gel testing. Also, the harsher recoil of the +P loads in lightweight J-frames tends to minimize practice efforts and decrease accuracy for many officers. The 158 gr +P LSWCHP offers adequate penetration, however in a 2" revolver the 158gr +P LSWCHP does not reliably expand. If it fails to expand, it will produce less wound trauma than a WC. Target wadcutters offer good penetration, cut tissue efficiently, and have relatively mild recoil. With wadcutters harder alloys and sharper leading edges are the way to go. Wadcutters perform exactly the same in both bare and 4 layer denim covered gel when fired from a 2" J-frame.
And DocKGR quoting from Dr. Martin Fackler's article: The Full Wadcutter--An Extremely Effective Bullet Design", Wound Ballistics Review. 4(2):6-7, Fall 1999):
"As a surgeon by profession, I am impressed by bullets with a cutting action (eg. Winchester Talon and Remington Golden Saber). Cutting is many times more efficient at disrupting tissue than the crushing mechanism by which ordinary bullets produce the hole through which they penetrate. The secret to the increased efficiency of the full wadcutter bullet is the cutting action of its sharp circumferential leading edge. Actually, cutting is simply very localized crush; by decreasing the area over which a given force is spread, we can greatly increase the magnitude to the amount of force delivered per unit are--which is a fancy way of saying that sharp knives cut a lot better than dull ones. As a result, the calculation of forces on tissue during penetration underestimate the true effectiveness of the wadcutter bullet relative to other shapes."
Doc KGR goes on at the link to recommend several JHPs for use in snubbies but most are +Ps. The one standard pressure JHP that he recommends is standard pressure Hornady Critical Defense. I'd use either that or some sort of hard cast full wadcutter in my snubby if it wasn't rated for +P. A Keith style semiwadcutter would be a second choice.