Abstract In this paper we study a natural generalization for the perfection of graphs to other interesting parameters related with colorations. This generalization was introduced partially by Christen and Selkow in 1979 and Yegnanarayanan in 2001. Let a , b ∈ { ω , χ , Γ , α , ψ } where ω is the clique number, χ is the chromatic number, Γ is the Grundy number, α is the achromatic number and ψ is the pseudoachromatic number. A graph G is ab-perfect if for every induced subgraph H, a ( H ) = b ( H ) . In this work we characterize the ωψ-perfect graphs.