The faster-Z/X hypothesis predicts that sex-linked genes should diverge faster than autosomal genes. However, studies across different lineages have shown mixed support for this effect. So far, most analyses have focused on old and well-differentiated sex chromosomes, but less is known about the divergence of more recently acquired neo-sex chromosomes. In Lepidoptera (moths and butterflies), Z-autosome fusions are frequent, but the evolutionary dynamics of neo-Z chromosomes have not been explored in detail. Here, we analyzed the faster-Z effect in Leptidea sinapis, a butterfly with three Z chromosomes. We show that the neo-Z chromosomes have been acquired stepwise, resulting in strata of differentiation and masculinization. While all Z chromosomes showed evidence of the faster-Z effect, selection for genes on the youngest neo-Z chromosome (Z3) appears to have been hampered by a largely intact, homologous neo-W chromosome. However, the intermediately aged neo-Z chromosome (Z2), which lacks W gametologs, showed fewer evolutionary constraints, resulting in particularly fast evolution. Our results therefore support that neo-sex chromosomes can constitute temporary hot-spots of adaptation and divergence. The underlying dynamics are likely causally linked to shifts in selective constraints, evolution of gene expression, and degeneration of W-linked gametologs which gradually expose Z-linked genes to selection.