Humans are often termed “cognitive misers” for their aversion to mental effort. Both in and outside the laboratory people often show preference for low-effort tasks and are willing to forgo financial reward to avoid more demanding alternatives. Mental effort, however, does not seem to be ubiquitously avoided: people play crosswords, board games, and read novels, all as forms of leisure. While such activities undoubtedly require effort, the type of cognitive demands they impose appear markedly different from the tasks typically used in mental-effort research (e.g., N-Back, demand selection tasks, vigilance tasks). We investigate the effect disparate demands such as rule discovery compared to rule implementation have on people’s aversion to or preference for increased mental effort. Across four experiments using three different tasks (i.e., N-Back, number sequence problems, and anagrams), and a mixture of online and lab-based settings we find that aversion to effort remains stable regardless of the types of cognitive demands a task imposes. The results are discussed in terms of other factors that might induce the pursuit of mental effort over and above the type of cognitive activity involved in a task.