  We study implications of recent data on neutrino mixing from T2K, MINOS,
Double Chooz and $\mu \to e \gamma$ from MEG for the Zee model. The simplest
version of this model has been shown to be ruled out by experimental data some
time ago. The general Zee model is still consistent with recent data. We
demonstrate this with a constrained Zee model based on naturalness
consideration. In this constrained model, only inverted mass hierarchy for
neutrino masses is allowed, and $\theta_{13}$ must be non-zero in order to have
correct ratio for neutrino mass-squared differences and for mixing in solar and
atmospherical neutrino oscillations. The best fit value of our model for
$\theta_{13}$ is $8.91\deg$ from T2K and MINOS data, very close to the central
value obtained by Double Chooz experiment. There are solutions with non-zero CP
violation with the Jarlskog parameter predicted in the range $\pm 0.039$, $\pm
0.044$ and $\pm 0.048$ respectively for a 1$\sigma$, 2$\sigma$ and 3$\sigma$
ranges of other input parameters. However, without any constraint on the
$\theta_{13}$-parameter above respective ranges become $\pm 0.049$, $\pm 0.053$
and $\pm 0.056$. We analyse different cases to obtain a branching ratio for
$\mu \to e \gamma$ close to the recent MEG bound. We also discuss other
radiative as well as the charged trilepton flavour violating decay modes of the
$\tau$-lepton.
