[Spidey'tilIDie]

OK, here's what I recall (up until New 52, I read all of JSA since its re-inception right after Grant Morrison's JLA took off.) Jesse originally was just a speedster following in her father's footsteps, although she alone had the power to fly. Later, after some issues with Wally wanting her to be the Flash and her not feeling up to it, she lost her ability to move at superhuman speeds (just like Wally did at one time.) She then visited her mother and discovered that she also inherited her powers (this was around the time the JSA was re-forming.) Shortly after they rechartered, she realized she still had both sets of powers. Most of her time in the JSA (spanning several years and more or less a hundred issues), she had both of their powers. Briefly, when asked to join Dick Grayson's Justice League (written by famed Starman writer, James Robinson), she re-claimed the mantle of Jesse Quick with both sets of powers. After Robinson's run on Justice League (17 issues featuring her), she went back to the JSA and Liberty Belle.