In this case we've had to fold the shirts in half lengthwise, because our carry-on bag is fairly narrow, but it'll be ok; vertical creases are more asthetically pleasing--don't ask me why.
The principle here is simple: by rolling our clothes we're creasing them less right from the start. We're creating a radius bend and we expect the fabric to recover from such gentle handling with just a bit of shaking out. It works.
