The purpose of this study was to investigate what experts in the use of picturebooks in mathematics education consider powerful characteristics of such books in the support of young children's learning of mathematics. The study started by investigating experts' views of such characteristics, as reflected in academic and professional publications on the use of picturebooks in mathematics education. This resulted in a first version of a framework of learning-supportive characteristics of picturebooks. In the second part of the study the framework was refined, and its tenability was tested through a four-round Delphi method, in which seven experts were asked to comment on, and work with, the framework when evaluating three picturebooks. The experts' evaluations of these books showed that a larger number of learning-supportive characteristics were identified when using the framework than when not using it.