Here's how to get Mathematica 10.2 to recognize MS Visual Studio 2015's C compiler (Windows 8.1).
	In the Mathematica installation folders, go to SystemFiles / Components / CCompilerDriver
	Make a backup copy of VisualStudioCompiler.m (for any disaster recovery)
	Open VisualStudioCompiler.m
	Scroll to $VisualStudioVersions and add "2015" to the list
	Scroll to installPath["2013"] and after it, include this new line 
                installPath["2015"] := installPathFromEnvironment["VS140COMNTOOLS"]
These hiccups bit me:
	Although I could edit VisualStudioCompiler.m, it wouldn't save to the above folder
	Instead, save it elsewhere and then copy it into the above folder
	It's not enough to simply install VS2015 -- once installed, within it you must yet install the C++ compiler 
	Once the C++ compiler is installed, open Mathematica and run:
        Needs@"CCompilerDriver`"
        CCompilers@Full
	You should see Visual Studio in the output list -- you're good to go
A big "Thank You" to those who led me to this solution.
Bruce
20150818