  The Painlev\'e analysis of a generic multiparameter N=2 extension of the
Korteweg-de Vries equation is presented. Unusual aspects of the analysis,
pertaining to the presence of two fermionic fields, are emphasized. For the
general class of models considered, we find that the only ones which manifestly
pass the test are precisely the four known integrable supersymmetric KdV
equations, including the SKdV$_1$ case.
