I try to work with client by next prince:
I do illustration/image/concept, client happy, he pay. And I continue work with next image and so on. If the customer is not satisfied in some reason, he don't lose his money I lose a bit time. This scheme also garantie safety for client if contingencies happened, and stability payment and trust relationship for me. Eventually when establishing trust relationships, client can paid after the completion the packet(5-10) of illustration or even whole work.
Sometimes, for example if need do just one illustration (or I first time see client), I can request prepaymant in amount of 25-50% of whole summ. But in most cases I worked in scheme that I describe above.
Briefly:
Payment — after each image is done.
If client new for me or need just one image - I can ask prepayment 25-50% (No refund)
If I know client (trust) can pay after a series of works performed
P.S: Sorry for my english :)