The solar s-process abundances have been analyzed in the framework of a Galactic Chemical Evolution (GCE) model. The aim of this work is to implement the study by Bisterzo et al. (2014), who investigated the effect of one of the major uncertainties of asymptotic giant branch (AGB) yields, the internal structure of the 13C pocket. We present GCE predictions of s-process elements computed with additional tests in the light of the suggestions provided in recent publications. The analysis is extended to different metallicities, by comparing GCE results and updated spectroscopic observations of unevolved field stars. We verify that the GCE predictions obtained with different tests may represent, on average, the evolution of selected neutron-capture elements in the Galaxy. The impact of an additional weak s-process contribution from fast-rotating massive stars is also explored.