Once you know there will be a written agreement, someone has to draft it. Should it be your lawyer or the other party’s lawyer?
Some say make your lawyer insist on preparing the first draft. I tend to agree with that. It gives you the opportunity to set the stage for later negotiations and control the language of the agreement. Whether he or she will suceed with that request depends on which of the parties has more bargaining power and whether the other side sees an advantage in preparing the first draft. If you are the party for whom most of the protections of the agreement are designed, for example a buyer in a purchase agreement or a lender in a loan agreement, you could argue that this fact alone should let your lawyer be the first drafter.
I think in many cases it is shortsighted to be afraid of the attorney’s fees for the first draft and subsequent revisions. In my experience, marking up a bad draft and checking on revisions often takes longer than drafting the whole thing in the first place. In particular, because your attorney should have pretty good samples to start with and thereby minimize the time to produce a good first draft.
Of course, sometimes it is just a matter of who was faster to seize the opportunity. A seller may present you with a draft very early in the negotiations and thereby make it harder to insist on a complete redraft.