  We present predictions for $\mu \to e \gamma$ and $\tau \to \mu \gamma$ in
the CMSSM in which there is a natural hierarchy of neutrino masses resulting
from the sequential dominance of three right-handed neutrinos. We perform a
global analysis of this model in the $(m_0,M_{1/2})$ plane, assuming radiative
electroweak symmetry breaking, and including all observed laboratory data. We
confirm that a large (small) $\tau \to \mu \gamma$ rate results from the
dominant right-handed neutrino being the heaviest (lightest) one. We show that
the $\mu \to e \gamma$ rate may determine the order of the sub-dominant
neutrino Yukawa couplings in the flavour basis, but may also be sensitive to
effects beyond the leading log and leading mass insertion approximations. We
also show that the $\mu \to e \gamma$ rate is independent of $\theta_{13}$, but
measurement of this angle may determine a ratio of sub-dominant Yukawa
couplings.
