Recently, I started taking a 3mg dose of melatonin for 1-3 days after flying to a timezone requiring a fair amount of effort to get a full night's sleep (3-6+ hours time difference), and find it helps to quickly get me on the new schedule. I maybe feel a little groggy, but nothing unsettling.

Note: I take a trip like this maybe once or twice a year (no more), and typically wake up with zero grogginess otherwise.