We exploit the versatility provided by metal-dielectric composites to demonstrate controllable coherent perfect absorption (CPA) or anti-lasing in a slab of heterogeneous medium. The slab is illuminated by coherent light from both sides, at the same angle of incidence and the conditions required for CPA are investigated as a function of the different system parameters. Our calculations clearly elucidate the role of absorption as a necessary prerequisite for CPA. We further demonstrate the controllability of the CPA frequency to the extent of having the same at two distinct frequencies even in presence of dispersion, rendering the realization of anti-lasers more flexible. © 2012 Optical Society of America.