The standard Engineer-Lawyer problem (Kahneman & Tversky, 1973) points to reasoners' failure to integrate mentioned base rate information as they arrive at likelihood estimates. Research in this area nevertheless presupposes that reasoners respect complementarity (i.e., participants ensure that competing estimates add up to 100%). A survey of the literature lends doubt to this presupposition. We propose that participants' non-normative performance on the standard problem reflects a reluctance to view the task probabilistically and that normative responses become more prominent as probabilistic aspects of the task do. Three Experiments manipulated two kinds of probabilistic cues and determined the extent to which a) base rates were integrated and b) the complementarity constraint was respected. Experiment 1 presented six versions of an Engineer-Lawyer-type problem (that varied 3 Levels of cue-to-complementarity and 2 base rates). Results showed that base-rate integration increased as cues-to-complementarity did. Experiment 2 confirmed that Gigerenzer, Hell & Blank's (1988) random draw paradigm facilitates base rate integration; a second measure revealed that it also prompts respect for complementarity. Experiment 3 replicated two of our main findings in one procedure while controlling for the potential influence of extraneous task features. Approaches that describe how probabilistic cues might prompt normative responding are discussed