i generally get about 25% of customers ask if I can leave an invoice, normally if they at work and they leave me the keys, which I don't mind, i think you have to be a bit flexible and friendly.
They normally pay up within the week, i think i've pehaps had one non payer in about 12 years, you can generally tell the ones that will try it on and look a bit dodgy :
If you are a bit more helpful, esp when people are busy then i think they will remember you for next time and use you.
regards
steve