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MadMonkey wrote: I'll be checking out the MP3 players soon. I wonder if a larger one would carry my iPhone AND the LCP or if it would end up being too thick... hmm....

A lot of them have a pocket in the front.
don't forget to look at GPS pouches too.
That's what I use when hiking. Holds Elsie Pea, GPS, phone, and a few other little things.

I'm no runner, but we do bike some.

You are on the right track with the MP3 player case. Go to Wal-Mart or any big store and look at all the options.
Do you suppose anyone would notice the lack of a wire coming from yours?
This would be the best option in my opinion.

Keltec makes a side clip for their P3At. I understand it also fits the LCP, perhaps with minor tweaking

Keltec also makes a neck lanyard. The ring mounts to a screw that replaces the plastic pin at the rear of the grip.
should fit that LCP also.

All of these are under $20, so try them all and pick the one that works best for you.

Personally, I could not run with a gun on my waistband. My pants would be around me ankles within a few steps.
If you have hips, you might have better luck ;)