  Levy-Loewner evolution (LLE) is a generalization of the Schramm-Loewner
evolution (SLE) where the branching is possible in a course of growth process.
We consider a class of radial Levy-Loewner evolutions for which sets of points
of the average means beta-spectrum can be found exactly. In this paper we show
how to overcome difficulties arised in previous works on multi-fractal analysis
of SLE/LLE.
