Do yourself a favour, and bill by the day, rather than by the hour. Engineering is creative work, and you're paid to think - code is just the end product. Thinking happens consciously and unconsciously, at all times of the day. Billing by the day will allow you to focus on the work rather than the administrivia.
Whatever you do, do not drop your rate: you'll just be undervalued by your clients.
Whatever you do, do not drop your rate: you'll just be undervalued by your clients.