In a series of experiments, Bott and Noveck (2004) found that the computation of scalar inferences, a variety of conversational implicature, caused a delay in response times. In order to determine what aspect of the inferential process that underlies scalar inferences caused this delay, we extended their paradigm to three other kinds of inferences: free choice inferences, conditional perfection, and exhaustivity in “it”‐clefts. In contrast to scalar inferences, the computation of these three kinds of inferences facilitated response times. Following a suggestion made by Chemla and Bott (2014), we propose that the time it takes to compute a conversational implicature depends on the structural characteristics of the required alternatives.