We complement our study of alpha/Fe enhanced stellar population models of Lick absorption indices ( Thomas et al. 2003) by comparing two sets of alpha/Fe enhanced models. In both models the impact on Lick indices due to alpha/Fe enhancement is accounted for through a modification of the stellar absorption line-strengths using the response functions of Tripicco & Bell (1995). One set of models, however, uses solar-scaled, the other alpha/Fe enhanced stellar evolutionary tracks. Since the alpha/Fe enhanced tracks are hotter than the solar-scaled ones (Salasnich et al. 2000), the correspondent stellar population models have slightly weaker metallic indices (i.e. Mg b, [Fe] etc.) and stronger Balmer line indices (Hbeta) (Maraston et al. 2003). Here we explore quantitatively the impact of this effect on the alpha/Fe ratios, metallicities and ages that are derived for elliptical galaxies. We find that the modest decrease of the metallic indices Mg b and [Fe] balance each other, such that fully consistent alpha/Fe ratios are derived for stellar systems using alpha/Fe enhanced models with either solar-scaled or alpha/Fe enhanced stellar tracks. The decrease of the metallic indices and the increase of Hbeta conspire in a way that also consistent metallicities are obtained. The derived ages, instead, are significantly different. The inclusion of alpha/Fe enhanced stellar tracks leads to the derivation of ages as high as similar to30 Gyr for elliptical galaxies. For the same objects, ages not older than 15 Gyr are obtained, if alpha/Fe enhanced models using solar-scaled tracks are adopted. This may indicate that current stellar evolutionary models overestimate the bluing of stellar evolutionary tracks due to alpha/Fe enhanced chemical mixtures at super-solar metallicities.