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Undercoverage plaques many frames - housing units are missed by listers or do not appear on the postal service list; persons with tenuous connections to households are not captured in rosters; persons hide their eligibility during screener interviews. The literature on undercoverage suggests several methods for improving the coverage of such frames, via a missed housing unit procedure, or detailed probes about household members, or disguising the target population in survey questions. However, each of these solutions introduces additional costs into the survey process. In this way, survey designers face a coverage-cost trade-off. In addition, there is increasing evidence that the cases found via these coverage-improvement measures are disproportionately nonresponders to the survey request. Thus there appears to be a coverage-nonresponse trade-off as well. Together these points raise the question of how much effort we should put into increasing coverage, when such efforts increase costs and nonresponse? This presentation will review empirical evidence for these trade-offs and search for clues to the mechanisms underlying the connection between nonresponse and undercoverage.