If you have several firms that handle similar kinds of matters, use their performance against budget to allocate work in the future.
The performance of each firm against their original budgets on matters should influence the likelihood of their being chosen to handle more matters. For example, if on a rolling average for the past three months one firm comes in 20 percent above budget, then their odds of being chosen for the next matter should shrink by 20 percent. The point is, if a firm manages costs well, it should get more work.
Managers of outside counsel will gag at this proposal. It will seem bizarrely quantitative, a bull in the china shop of what they see as their intuitive, subjective, multi-faceted artistry of selecting the right firm.