You need to figure that the first five shots (or whatever S&W fires for proofing and function checking) are going to be on new Melonite or chrome. These first shots will be like rubbing the bullets over fine sand paper until the finish smooths out.

I don't believe in the shoot one and clean theory of break in. That's another topic and doesn't affect chromed or Melonite finished barrels anyway. What I have noticed is that it usually take a minimum of 40 shots for a rifle barrel to settle down and start shooting respectable groups.

Run a couple of patches down the bore, go to the range, put a couple of boxes of ammo down range, clean, and repeat.