We propose a two-stage choice model in which decision makers first filter out alternatives (consideration stage) before choosing their preferred alternative among the considered options (choice stage). The model accounts for heterogeneity in consideration screening by allowing respondents to have different thresholds for accepting attribute levels. By utilizing a conjunctive consideration rule, the model can capture well-known non-compensatory screening heuristics. The decision stage is modelled with a compensatory utility model. We compare our two-stage approach with the mixed logit model on simulated choice data, and conclude that both models can be distinguished based on the pattern of opt-out responses they produce. If such responses are the result of screening behaviour, the two-stage model is always selected in favour of a single-stage model. In addition, we evaluated several models on empirical choice data concerning preferences towards cinemas. Our results show that the data is best explained by the proposed model, suggesting that 73% of the participants used a screening rule before making a final choice.