Can unstable relics save pure Cold Dark Matter?

The standard CDM model fails to describe the power spectrum of fluctuations since it gives too much power at small scales. Among other possible improvements, it has been suggested that an agreement with observations can be achieved with the addition of a late decaying particle, through the injection of non-thermal radiation and the consequent increase of the horizon length at the equivalence time. We analyze the possibility of implementing this idea in some extensions of the electroweak standard model, discussing the cosmological and astrophysical bounds to which these schemes are subject.