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This article addresses simultaneously two important features in random utility maximisation (RUM) choice modelling: choice set generation and unobserved taste heterogeneity. It is proposed to develop and to compare definitions and properties of econometric specifications that are based on mixed logit (MXL) and latent class logit (LCL) RUM models in the additional presence of prior compensatory screening decision rules. The latter allow for continuous latent bounds that determine choice alternatives to be or not to be considered for decision making. It is also proposed to evaluate and to test each against the other ones in an application to home-to-work mode choice in the Paris region of France using 2002 data.