  We complete the mathematical analysis of the fine structure of harmonic
measure on SLE curves that was initiated by Beliaev and Smirnov, as described
by the averaged integral means spectrum. For the unbounded version of
whole-plane SLE as studied by Duplantier, Nguyen, Nguyen and Zinsmeister, and
Loutsenko and Yermolayeva, a phase transition has been shown to occur for high
enough moments from the bulk spectrum towards a novel spectrum related to the
point at infinity. For the bounded version of whole-plane SLE studied here, a
similar transition phenomenon, now associated with the SLE origin, is proved to
exist for low enough moments, but we show that it is superseded by the earlier
occurrence of the transition to the SLE tip spectrum.
