Leave it be! It has gone into transplant shock, and may take a week or two to recover. This is perfectly normal for almost any plant.

Don't know how it's going to go with the rocket, however! In its present state, it may well lose the battle for survival against a lot of formidable opponents.

Yes, I agree not to disturb it. No matter how well plants are handled, once their soil is disturbed, the plants do get shocked and could die. Adding to that, another transplanting and you have probably killed it. Just don't overwater now, as that will also harm it. If your doing a lot of plant moving and transplanting, suggest you find a good transplating additive. I use one here that is mixed with water, and is syrupy. It contains many things, including vitamins to help the moved roots to overcome being seriously damaged. Some roots are microscopic and are not seen by the naked eye.
I have sucessfully transplanted many one inch tall tomato and pepper seedlings, that don't even have true leaves yet. These are actually yanked out of the soilless medium and dropped into new holes in empty pots of soilless mix. Its usually after I had accidentially dropped in too any seeds in a single pot, and the plants begin to sprout.

May I suggest that you keep it out of direct sun for a few days? A transplanted basil, or any other plant, has a lot going on and can't handle a lot of direct sunlight and/or heat for a few days after being moved from one pot to another. When transplanting from one outdoor site to another place, I usually erect a newspaper tent over the newly moved plant to protect from sun and wind. It's easier with a potted plant--just put it in a sheltered spot in the garden or the house, and let it recover.

ok... the purple basil is doing better now. I pulled off a pair of drooping leaves yesterday (it had 4, including a developing pair). Today the other slightly droopy leaves seemed to have recovered, and I think there might even be some branching action going on... do they really recover THIS FAST?

The roots were exposed to air for a good while (5 minutes to say the least), and again between the second transplant. Though it is in its own pot now... I gave it 3 hours of Jack Johnson and classical music and left it indoor today, I guess I'll try to leave it outside tomorrow, under shades, of course.

Anyone who would like to put in additional comments?

Don't remove any of the wilted leaves (unless they're dead, of course). Just leave the plant be for a while. Think how you'd feel after a transplant operation. Just because you feel a bit wilted, it doesn't mean that chopping off that very tired and heavy arm is going to help you recover more quickly! It could well strengthen with time.

Yes, a plant can recover quickly, but not if it's killed with kindness!! Basil, of course, being an annual, is always going to grow fast.

Plants do like music, but not all music. I've never heard of Jack Johnson, so I can't comment on that, but I do know, from my readings, that plants actually prefer Baroque music. They don't like very loud music, and have a definite preference for instrumental classics (as in 18-19th Century stuff).

Leave it alone, let it rest!! Killing with kindness is the worst way to do in plants. Plants have no easy way to communicate if they are not being treated propely. They either curl up and die, or look just fine one day and dead the next. Just check for any water needs every few days and keep it warm and with lots of light. If its under plant lights, they need about 18 hours of it. The plants do need darkness too, but only a few hours if they are indoors. I never remove any leaves, even if they are showing signs of dieing. Let them fall off on their own.