If you ask three or four firms to propose their approach, staffing and budget for a new matter, each firm being capable of handling the work and each firm knowing their competitors for the work, you will save outside-counsel fees just for doing that (See my post of Aug. 5, 2007 about how to prove savings from a fixed fee arrangement.). The competition will reduce your costs.
Each firm is likely to temper its billing enthusiasm because it wants to get the work and not have a peer snatch it away. That competitiveness plus market discipline, without anything more, will reduce fees over time because if nothing else were to change, the firm you select has at least some sense of accountability to its budget estimate.
No way, cynics might respond; law firms blow through budget estimates without a moment’s pause or embarrassment. Possibly, but a firm that cares about building the breadth and depth of its services to a law department over time does not as lightly run roughshod over its recently-submitted budget. And, a disciplined law department that observes nothing material to have changed the budget, can hold the law firm to its forecasted amount.