We clarify some aspects related to critical phenomena in 1D coupled map lattices. In particular, we explain why a model studied by Chaté and Manneville did not seem to be in the same universality class as directed percolation, contrary to first expectations. We claim that this model is actually in this universality class, but that scaling is extremely late. We present a slightly modified model which seems to be in this universality class with respect to some properties but not all. In contrast to directed percolation and to the model studied by Chaté and Manneville, our model shows a very complex sequence of singularities vaguely reminiscent of the richness of bifurcations in 1D maps.