A few companies in America have such name recognition that almost any law firm squirms and sweats to be able to represent them. The larger the law firm, though, the less even a headline client softens their billing policies though a smaller firm will still covet a prestige client and jump through hoops.
The sophistication of the legal work given to a firm may sound like an inducement, but it may have the opposite effect on billing terms. If you ask for services of the most specialized lawyers, you are unlikely to get fee discounts and alternative arrangements (See my post of Feb. 12, 2006 about the bargaining power of the few acceptable firms in several capital cities.). Why should busy experts bend, unless they can delegate?
There may be a slight advantage to being a brand new client, but I doubt that it is more than a tremor.
A firm my grant favorable financial terms if a prospective client dangles a chance to enter a new field or extend services in a familiar field. That opportunity has some value to a firm, and might loosen the purse strings a bit.
My hunch is that the most influential new client is one that moves the revenue needle relatively the most in a law firm. Naturally, a $250,000 matter commands more attention at a small firm than at a national firm.
All of the foregoing must be tempered by the realization that it is usually a single partner, and their attitude toward new work, that carries the day – not a “law firm” decision.
At bottom, consistently large dollars, relative to the size of the firm, outmatches cachet, legal sophistication of the work, another notch in the belt, or professional growth as an influencer of billing policy.