We study the following problem: for given integers d,k and graph G,can we reduce some fixed graph parameter π of Gby at least d via at most k graph operations from some fixed set S? As parameters we take the chromatic number χ,clique number ω and independence number α, and as operations wechoose edge contraction ec and vertex deletion vd. We determine the complexity of this problem for S = {ec} and S = {vd} and π ∈ {χ, ω, α}for a number of subclasses of perfect graphs. We use these results to determine the complexity of the problem for S = {ec} and S ={vd} and π∈{χ, ω, α} restricted to H-free graphs