During a year, the total number of law firms a law department paid matters less than the concentration of its spending. If a department moves from 200 law firms to 100 law firms but distributes its spending evenly among those 100, it has missed an opportunity to improve. If the department converges from 200 law firms to 150, but pays the five firms paid the most 75 percent of its spending, then it has an opportunity to explore with those firms alternatives to hourly billing and other cost-saving efforts. The key idea is not convergence but rather concentration.
When seeking to control outside counsel costs, a misguided step is certainly step-wise rate reductions. With such a reduction scheme, a law department gets larger rate reductions the more it spends on a law firm. It sounds plausible as you are getting volume discounts at increasing levels. The disadvantage is that the law department may find itself pressured to give work to a firm in order to reach higher discount levels, rather than because the firm will do the best job on the matter. Discounted rates on of average quality work gains nothing.