The CV method estimate the monetary value that specific changes in the provision of goods and services represent for society, which is asked for their Willingness To Pay (WTP) for it, according to their budget and individual preferences, in a survey. The applications of CV are a source of information to important public decision-making. Therefore, it seems to be a desirable objective for a CV study to strive to detect and reduce, as far as possible, the bias affecting the elicited values. In the present work, the starting point bias in an application to the case study of the conservation of the Iberian Lynx in Spain is analyzed. This bias is caused by the potential influence of the bid values offered to the interviewees on their stated preferences. Three different but related issues are treated. Firstly, data obtained from a pretest survey are used to generate a bid design that distort as less as possible the real preferences of the population, on the basis of the choice of the starting points and the proportions that will be presented to the interviewees. Secondly, data obtained from the complete survey are analyzed, proving that, in effect, the stated WTP are clearly related to the used starting point. And finally, some carried out simulations show the direction and intensity of the influence of different bid designs on the mean population WTP. Results support the idea of the great importance of the questionnaire design and posterior analysis which enables us to identify and minimize the starting point bias before the estimation of social benefits.