Can a well-crafted set of interrogatories ever hurt your case?
In many complex cases, interrogatories served early in the case can educate your opponents about your case strategies at a time when you'd rather keep them in the dark. Moreover, when you serve the interrogatories on your opponents, you are requiring them to get up to speed on their own case strategies, perhaps sooner than they would have done so otherwise.
For these reasons, some lawyers like to depose the key witnesses before serving any but the most basic interrogatories. The idea is that you will deprive these witnesses (and your opposing lawyers) from some of the early-stage strategizing that often allows them to rehearse their answers in advance. With an element of surprise, you're more likely to get spontaneous and unrehearsed admissions.
Try it sometime and see if it works for you: depositions before interrogatories.
Source: Kenneth R. Berman, "Q: Is This Any Way to Write an Interrogatory? A: You Bet It Is," from Litigation magazine, reprinted in The Litigation Manual: Pretrial (ABA).