In contingent valuation surveys, there is a range of possible explanations for zero bids, from true zero responses consistent with economic decisions to protest responses. According to the empirical literature, which analyzes the determinants of willingness-to-pay (WTP) values from a bidding process, the double-hurdle is the most appropriate econometric approach to account for zero and protest WTP. However, when the number of protest responses is too small to be explicitly modelled, this approach is not applicable. This frequently occurs in critical health care situations, where large samples are not easily available. We discuss the possible econometric strategies for use in such cases. For illustrative purposes, the different models were applied to an empirical situation, which refers to the location preference (i.e. home versus hospital) from French cancer patients for blood transfusion. Our results show that protest responses should not be discarded, even if present in small numbers, and that the type II Tobit and the standard truncated regression model could both be applied. However, since from small finite samples, the most robust estimation is obtained from the bootstrap method with a high number of replications, the truncated regression model, easily applicable, weakly computer time-consuming and not subject to identification problems in this case contrary to the type II Tobit, should be the econometric strategy of choice for various WTP studies in the healthcare field.