This paper discusses the estimation of choice models on pivot-style stated choice data sets that include a reference alternative that corresponds to a recent trip by a respondent. With the potentially high levels of inertia observed in many such data sets, the questionnaire for the current survey gave respondents a secondary choice between the purely hypothetical alternatives when they gave preference to the reference alternative. The aim of this paper was to investigate appropriate ways to deal with such a dual-response data set at the modeling stage. The analysis shows only small differences in scale and willingness-to-pay estimates between the primary and secondary choices, suggesting that especially in the presence of large amounts of inertia in primary choices, secondary responses may provide analysts with useful information on sensitivities.