Analytic QCD coupling with no power terms in the UV regime

We construct models of analytic QCD (i.e. with the running coupling parameter free of Landau singularities) which address several problems encountered in previous analytic QCD models, among them their incompatibility with the ITEP-OPE philosophy (due to UV power terms) and too low values of the semihadronic tau decay ratio. The starting point of the approach is the construction of appropriate nonperturbative beta functions.