I know how to change bike tires. I watched my father do it when I was ten years old and the guys at the local bike shop make it look easy. So I never went for a ride without tire levers and a spare inner tube or two.
Unfortunately, knowing how and actually doing it can be two different things. They say to put the tire back on over the rim with just your hands, because using a metal tool may pinch your new tube or poke a hole in it. With some tire and rim combinations, it’s close to impossible, and becomes less possible as you reach those last few inches of bead and your hands get tired and sore. You’ll be stranded until you get that tire bead over the rim.
The Kool Stop Tire Bead Jack is the lightweight, inexpensive answer to this problem. Just put the fixed end on the other side of the rim, hook a section of bead and use the handle to pull it up over the rim. Repeat as needed, and in a few seconds, you’re done and on your way.
It’s too long to fit in a small tool kit. It’s about the length of a CO2 pump, but it’s not metal so it’s very light. You can stick it in a handlebar bag, or a rack trunk or just strap it to your top tube. You won’t want to ride far without it.