I did two and a half weeks in Thailand with a 22" and a carry-on. It's definitely do-able if you limit shoes (one pair for walking, flip-flops for the beach/pool) and have your laundry sent out at least once along the way (it's pretty cheap in most of Asia).

I also used super-lightweight fast-drying tropics pants from Travelsmith, which took up much less space in my bag and I could rinse out every night and have dry by morning.

My 22" was expandable, and despite discarding some clothes along the way I filled it with enough gifts that I had to expand and check it on the return. I also sent a package home from Bangkok (with gifts and a pair of shoes I had taken with me but wasn't using much); the hotel was happy to box and mail it for me and I recall the postage being quite reasonable.