Goosh: Your Sig looks pretty rotten - if it was Russian Glass, I'd blame a Bad Vodka Day. My other cheap-ish wide-ish fast-ish lenses (Zenitar 16/2.8, Albinar 21/3.5, Vivitar 24/2.0) are nowhere near that bad. (My Vemar 12/8.0 is worse, but it was built wrong.) I've rather lusted after a Mir 20/2.5 myself, so if you get it, let us know what's what.
Ira: My Mir-1B 37/2.8 (without the Grand Prix icon) is M42, came in a nifty clear-plastic screw-down-the-lens case. But LOTS AND LOTS of Russian Glass was made for L39 (USSR Leica-clones) and M39 mounts. M39-M42 adapters are cheap and easy to find. But if your Mir has a L39/LTM mount, you're screwed, Pentax-wise. Leica and Pentax registers (lens-to-sensor distance) are vastly different, and in the wrong direction. A Pentax lens
*could* be fitted to a Leica-LTM mount, but not vice-versa. See here:
http://www.graphics.cornell.edu/~westin/misc/mounts-by-register.html
There's an easy way to find out if your Mir is LTM/L39 or M39. Remove whatever lens is on your camera. Focus the Mir to infinity and hand-hold it up to the camera mount. Look thru the viewfinder. Aim at some distant object. Move the Mir around a little. If the distant object comes into focus, even briefly, you've got a M39 and it's worth getting an adapter. If everything you see is beyond blurry, too bad. I only have 7 such lenses that I can't use.
EDIT:
Ryan: The usual reason for M39 or M42 lenses (like the Jupe you mention) not hitting infinity is from using a flanged K-M42 adapter, which pushes the glass out
just enough to be shortsighted. Some long teles, like my Spiratone 400/6.3, actually far-focus
past infinity, so the flanged adapter corrects that. Flangeless adapters (sometimes labeled INFINITY FOCUS) like those from Pentax and Bower, don't have that problem. Of course, if you're using the Jupiter-9 for portraits, you don't really
need infinity, right?