  We derive new constraints on the quantities delta_{XY}^{ij}, X,Y=L,R, which
parametrise the flavour-off-diagonal terms of the charged slepton mass matrix
in the MSSM. Considering mass and anomalous magnetic moment of the electron we
obtain the bound |delta^{13}_{LL} delta^{13}_{RR}|<0.1 for tan beta=50, which
involves the poorly constrained element delta^{13}_{RR}. We improve the
predictions for the decays tau -> mu gamma, tau -> e gamma and mu -> e gamma by
including two-loop corrections which are enhanced if tan beta is large. The
finite renormalisation of the PMNS matrix from soft SUSY-breaking terms is
derived and applied to the charged-Higgs-lepton vertex. We find that the
experimental bound on BR(tau -> e gamma) severely limits the size of the MSSM
loop correction to the PMNS element U_{e3}, which is important for the proper
interpretation of a future U_{e3} measurement. Subsequently we confront our new
values for delta^{ij}_{LL} with a GUT analysis. Further, we include the effects
of dimension-5 Yukawa terms, which are needed to fix the Yukawa unification of
the first two generations. If universal supersymmetry breaking occurs above the
GUT scale, we find the flavour structure of the dimension-5 Yukawa couplings
tightly constrained by mu -> e gamma.
