[I've done the same, but presented my less useful hours as discounted from the usual rate.]
Arguably your scenario sets up two incentives which may not be a good thing.
First, you are incented to concentrate on High Value and disregard Low Value. Maybe that's not what your customer wants from you - they need you to go to meetings which in fact they regard as Equal Value.
Second, your customer when acting naively (think Pointy Haired Boss) is incented to give you Low Value work to rein in your billing - so you never get anything useful done.