Generally, for the first 1 or 2 hours, I charge full rate. Anything after that, the rate goes down significantly.
I also do not charge for un-productive time. For instance, if I spend 30 minutes working on a solution that does not produce results, and have to go back and spend another 15 minutes on something that DOES work, I only charge for the 15 productive minutes.
I also tend not to charge for time where the computer is doing a procedure, and I am just sitting there watching it.
The big picture, as I have told all of my other clients, is that my personal and business relationship to you is more important than the almighty dollar.
I would rather walk away after 2 hours work, and only spend 30 minutes of "billable time", and have you satisfied, than hackle over what I charged for.
I look forward to working with you.