All surveys with less than full response potentially suffer from nonresponse bias. Poststratification weights can only correct for selection into the sample based on observables whose distribution is known in the population. Variables such as gender, race, income, and region satisfy this requirement because they are available from the U.S. Census Bureau, but poststratification based on these variables may not eliminate nonresponse bias. I develop an approach for correcting for nonignorable nonresponse bias. Survey respondents can be classified by their "response propensity." Proxies for response propensity include the number of attempted phone calls, indicators of temporary refusal, and interviewer-coded measures of cooperativeness. We can then learn about the population of nonrespondents by extrapolating from the low-propensity respondents. I apply this new estimator to correct for unit nonresponse bias in the American National Election Study and in a CBS/New York Times preelection poll. I find that nonresponse bias can be a serious problem, particularly for items that relate to political participation. I find that my method is successful in substantially reducing nonresponse bias.