A recent proposed model showed that the impedance of a film with a uniform permittivity and a resistivity that varies along its thickness according to a power-law is in the form of a constant phase element (CPE). This model is further considered in order to assess the effect of non-uniform permittivity profiles. It is shown that a power-law permittivity profile is also compatible with a CPE behavior when resistivity and permittivity vary in opposite ways along the film thickness. This work shows that, for important classes of materials which show CPE behavior, relaxation of the assumption of a uniform permittivity does not alter the conclusions developed in the earlier work, and the formula relating film properties to CPE parameters is shown to apply.