Current data on the luminosity function of nearby stars allow the possibility that the stellar initial mass function (IMF) is double-peaked and that the star formation rate (SFR) has decreased substantially with time. It is then possible to account for all of the unseen mass in the solar vicinity as stellar remnants. A model for the solar neighborhood has been constructed in which the IMF is bimodal, the SFR is constant for the low-mass mode and strongly decreasing for the high-mass mode, and the mass in remnants is equal to the column density of unseen matter; this model is found to be consistent with all of the available constraints on the evolution and stellar content of the solar neighborhood. In particular, the observed chemical evolution is satisfactorily reproduced without infall. The total SFR in the model decreases roughly with the 1.4 power of the gas content, which is more plausible than the nearly constant SFR required by models with a monotonic IMF.