Several studies investigated preschoolers' ability to compute scalar and ad-hoc implicatures, but only one compared children's performance with both kinds of implicature with the same task, a picture selection task. In Experiment 1 (N = 58, age: 4;2-6;0), we first show that the truth value judgment task, traditionally employed to investigate children's pragmatic ability, prompts a rate of pragmatic responses comparable to the picture selection task. In Experiment 2 (N = 141, age: 3;8-9;2) we used the picture selection task to compare scalar and ad-hoc implicatures and linked the ability to derive these implicatures to some cognitive and linguistic measures. We found that four- and five-year-olds children performed better on ad-hoc than on scalar implicatures. Furthermore, we found that morphosyntactic competence was associated with success in both kinds of implicatures, while performance on mental state reasoning was positively associated with success on scalar but not ad-hoc implicatures.