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.Comment: 12 pages, 5 figures, revised version (short changes in the text,
Refs.[21,22,23] are new), version as it appears in J.Phys.G37,07500
