1. Remember that not all writing has to be graded or even collected.  You don't need to collect their writing at each stage of the writing process—only to monitor student progress at what you think are the most important moments in it.  Even if you don't intervene, students are likely to improve.
  2. Make substantial formative responses to one early draft to give students a sense of your criteria for writing.  After the first draft, make your commentary far briefer and more summative.  In this way requiring two or more drafts of an assignment should only slightly increase your workload.
  3. Consider putting off grading completely until the end of the term, or until students have received formative feedback from peers and you, and then base grades on the revisions students have made to earlier feedback.
  4. Put strict bounds on the revision process.  Allow students to revise their papers only if they meet with you first, only within a certain time period, or only if they attach peer critiques from two of their classmates to the revised draft.  Or require/allow revisions only from students whose writing falls below a certain threshold on your rubric.