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I run allot, including weekly long runs in the 2-2.5 hour range currently. I prefer to carry and wear as little as possible which makes a fanny pack of any type pretty much unbearable. I have had ok luck with a bellyband and my small Ruger LCP, my cell phone and CHL in one of the pockets. I am lean and my "medium" Bellyband holster is a bit too large but some extra velcro and a safety pin solved that. It is reasonably comfortable, so far in cold to warm conditions but I have my doubts about it for weather in the 90's+
It is wide which adds to it's stability and could presumable carry a larger gun but I wouldn't want to run with my Glock or anything bigger than a pocket pistol. The wide fabric on me, 5'10 172 lbs covers alot of flesh and interferes a little with my HR strap but for runs in the ten mile or less range it has been ok.
For casual runners or "joggers" the fanny pack is probably suitable, there is no easy solution for running/cycling outside in the Summer and of course my swim training leaves me disarmed and in a state of sensory deprivation, sometimes you make compromises and do the best you can.
I have what is commonly called a "Bento Box" on the top tube of my road and triathlon bikes that can hold the same small pistol and a couple of cliff bars on my bike but it is off body carry not optimal. Carrying it in a jersey pocket it will get sweaty plus the weight tugs the jersey around awkwardly and leaves a pretty clear pistol outline on the fabric, as you can imagine there is no room in cycling shorts for any weapons other than what I was born with.