A unit billing arrangement is similar to a flat-fee arrangement but for a specific task rather than an entire matter (See my post of April 5, 2006 defining and contrasting fixed and flat fees.). For example each deposition could be billed at a set unit rate.
Unit billing is best used when the typical time to complete a task can be determined and the client agrees on the value of the task, such as a single trademark clearance in the US, or incorporation of a shell entity in Delaware.