This communication focuses on the effective permittivity of a mixture that consists of a background medium in which layered spherical scatterers are randomly embedded. For dense nontenuous media, the quasicrystalline approximation has to be supplemented with the coherent potential approach. For the effective permittivity or the effective propagation constant, two theories have been published [1,2]. This paper compares the predictions of these theories and proves that they are consistent.