It's pretty much a given that savvy police officers often carry a second handgun to back up their primary service auto. I believe that the second gun needs to be very similar to the primary in its handling and operation. In my day, this requirement was most commonly manifested with a Model 19 (or 15) in the holster with a 2-inch Model 36 (or 42) in hiding. Under stress, the similar loading, handling and firing was very comforting. But now that the police service revolver is pursuing the Dodo bird, this practice seems to be falling into disuse. It doesn't need to. In fact, there is more reason than ever to pair up the service handgun with a hideout pistol of the same make and/or similar handling.
The biggest reason for doing this often goes unnoticed. Much of the time, the longer magazine of the full-sized holster gun can be used in the shorter backup gun. This simply means that a badly jammed or broken holster gun can be replaced with the hideout pistol and reloaded with magazines for the bigger gun. The shooter needs to understand that this is an emergency procedure only, in that an excessively long magazine can be damaged by violent magazine changes that drive the magazine into the underside of the slide. Whatever the action style of the holster gun—DAO, DA/SA, SA etc.— the backup needs to be an available model with the same lockwork from the same maker. There are many possibilities.
How about a SIG P226 (a full-size auto in .40 S&W) backed up by a P229 in the same caliber? A S&W M&P pairs beautifully with an M&P Compact in four different calibers—9 mm, .357 Sig, .40 S&W and .45 ACP. Glock has a number of models that compliment well—G17 and G19, G22, G23 and others. There are even some even-smaller third options in the Glock line. There may be some other makers in the race, but the latest is Ruger with their SR9 and SR9c 9 mm pistols with the long magazine usable in the short gun. I have to believe this is a sales point the company is neglecting.
Finally, may I point out that the greatest of the modern handguns, John Browning's immortal 1911 Colt, actually fits into this limited category. If the shooter carries either the Government Model or Commander using a 7-shot or 8-shot magazine, he or she can back up with several different short-slide, short-butt models from Colt—CCO, Officer's ACP and Defender. These guns may use a shorter magazine to go with their short butts, but they will work with same magazines as were in use since 1911.
