How to build one Linux binary for many i386 platforms

I would like to build one Linux binary set--binary apps and any buttociated dynamic libraries--for many Linux i386-based platforms (at least RHEL 3.x-4.x, Fedora Core 2,3,4,5, Debian 3.1, but would like sever more). I may still make multiple *package* distributions (eg, .rpm, .deb etc), but I would like to have one build process provide the binary-file-set input to these packages.

How does one effectively do this?

I see application distributions like these doing this:

(I recall there being many others, I just don't have references to them at the moment.)

How is this done? Is it a careful management of std-library-kernel-library dependence? I'm sure it is, but I'm not sure exactly how to go about controlling this. Is there a reference I can read somewhere? Is it mostly a matter of constructing the "least common denominator" build systems from which to link the "most ubiquitous" library set? Do I need to build the libstdc-2.x-libstdc++-* on a Linux machine and compile to that?

I suspect this is a faq that's been answered somewhere; I have yet to find the answer.

My project is a C++-based one. Does this have a bearing on my library depedence? (eg, libstdc++...so?)

Thanks for any help, -Matt -- Remove the "downwithspammers-" text to email me.