This article addresses the important issue of anchoring in contingent valuation surveys that use the double-bounded elicitation format. Anchoring occurs when responses to the follow-up dichotomous choice valuation question are influenced by the bid presented in the initial dichotomous choice question. Specifically, we adapt a theory from psychology to characterize respondents as those who are likely to anchor and those who are not. Using a model developed by Herriges and Shogren (1996), our method appears successful in discriminating between those who anchor and those who did not. An important result is that when controlling for anchoring - and allowing the degree of anchoring to differ between respondent groups - the efficiency of the double-bounded welfare estimate is greater than for the initial dichotomous choice question. This contrasts with earlier research that finds that the potential efficiency gain from the double-bounded questions is lost when anchoring is controlled for and that we are better off not asking follow-up questions.