Another option is to fly Delta Air Lines all the way to Singapore and take either Tiger Airways or AirAsia for the short 95-minute flight to Phuket.

I have flown as a passenger on both airlines, and both offer clean, basic no-frills service for low airfares — especially when there is an airfare sale. The flights I took departed and landed on time. Just watch out for the extra fees, which are easily avoidable.