Galaxy number counts at faint magnitudes exceed the expectations from non-evolving models, based on the present-day galaxy population, by a large margin. Despite this, redshift surveys show that the redshift distribution is as expected in the non-evolving case, lacking in particular the tail of evolved bright galaxies at high z predicted by the standard evolutionary models. We consider here the effect of using a broadly peaked, rather than steadily rising, luminosity evolution model. Evolution of this form has as its physical basis current infall models for the history of star formation in our Galaxy. Incorporation of this evolution - which has the key attribute of a relatively modest yet broad peak, occurring relatively recently - in an otherwise standard population model can account for the apparently non-evolving z distribution, while at the same time giving reasonable agreement with the observed number counts. This occurs because the `extra' galaxies are not at excessively high z (i.e. large look-back time), since the evolutionary brightening at early times is small or even negative.