I ride a road bike and carry a Topeak pump that's bigger than a mini but smaller than a full-sized frame pump. This is because my frame is a GT and a full-size frame pump is not compatible. Thankfully I don't get a lot of flats, but when I do the mid-size Topeak pump works well.

You can see the pump mounted on the seat tube in this photo. Topeak calls it a "Speed Master Blaster" but it's not all that fast!
Rick / OCRR