Slim gun for running

Hey ladies who carry when they run.. so my fiance carries a p365 in her day to day life in a crossbody bag. I bought her a belly band but she’s 5’3” 95lbs so the gun sticks out farther than her breasts and makes it very noticeable. She went out for a jog and wasn’t a fan. I’ve considered getting her a small 22lr for her jogging but just seeing what you guys do. Is there good fanny pack you run with also?