In the early 1990s Henri Cohen and Jacques Martinet offered a probabilistic model that explains the behaviour of ideal class groups of number fields in natural families, generalising earlier work by Cohen and Lenstra. There is a lot of numerical evidence for the correctness of the model, but very few theorems. In joint work with Hendrik Lenstra we revisit the Cohen-Martinet heuristics and, among other things, disprove them in two different ways, but also lend additional support for the expectation that they are "basically true". In this talk I will explain one of these disproofs, and will propose possible corrections.