We study the rank–2 distributions satisfying so-called Goursat condition (GC); that is to say, codimension–2 differential systems forming with their derived systems a flag. Firstly, we restate in a clear way the main result of[7] giving preliminary local forms of such systems. Secondly – and this is the main part of the paper – in dimension 7 and 8 we explain which constants in those local forms can be made 0, normalizing the remaining ones to 1. All constructed equivalences are explicit. The complete list of local models in dimension 7 contains 13 items, and not 14, as written in[7], while the list in dimension 8 consists of 34 models (and not 41, as could be concluded from some statements in[7]). In these dimensions (and in lower dimensions, too) the models are eventually discerned just by their small growth vector at the origin.