This paper presents the development and estimation of a novel semi-compensatory model for residential choice. The model assumes that apartment seekers engage in a two-stage process, consisting of a non-compensatory strategy to retain only alternatives that meet search-criteria thresholds, followed by a compensatory strategy to finalize the choice. The first stage is represented by hierarchically correlated ordered-response models and the second stage by a multinomial logit model. The model estimation on data retrieved from a real-estate website, designed to track two-stage choice protocols, reveals the determinants of threshold selection and apartment choice. Results show that (i) threshold selection depends on individual characteristics, (ii) the proposed model is applicable to choice contexts with many alternatives, making it unique in the literature of semi-compensatory models and especially suitable for modeling residential choice, and (iii) the proposed model outperforms the compensatory model and reveals an upward bias in the parameters of the latter.