A multivariate modified histogram density estimate depending on a reference density g and a partition P has recently been proved to have good consistency properties according to several information theoretic criteria. Given an i.i.d. sample, we show how to select automatically both g and P so that the expected L 1 error of the corresponding selected estimate is within a given constant multiple of the best possible error plus an additive term which tends to zero under mild assumptions. Our method is inspired by the combinatorial tools developed in Devroye and Lugosi [1] and it includes a wide range of reference density and partition models. Results of simulations are presented.