Past approaches to correcting for unit nonresponse in sample surveys by re-weighting the data assume that the problem is ignorable within arbitrary subgroups of the population. Theory and evidence suggest that this assumption is unlikely to hold, and that household characteristics such as income systematically affect survey compliance. The authors show that this leaves a bias in the re-weighted data and they propose a method of correcting for this bias. The geographic structure of nonresponse rates allows them to identify a micro compliance function, which they then use to re-weight the unit-record data. An example is given for the U.S. Current Population Surveys, 1998-2004. The authors find, and correct for, a strong household income effect on response probabilities.