A dichotomous Case-Based Reasoning (CBR) model is one in which two kinds of reasoning mechanisms are employed for realizing fast and slow problem-solving as demanded by the nature of the incoming query. This is inspired by Daniel Kahneman's seminal work on the two modes of thinking observed in humans. In this paper, we present the following three directions of refinement for a dichotomous CBR model: selection of attributes for a fast thinking model based on parsimonious CBR, switching from fast to slow thinking based on constraints derived from domain knowledge and arriving at a complexity measure for evaluating dichotomous models. For all the three improvements identified, we discuss the results on real-world data sets and empirically analyse the effectiveness of the same.