From Huber's "Robust Statistics" book:

"As starting values (\theta^(0), \sigma^(0)), we usually take the ordinary least squares estimate, despite its known poor properties [cf. Andrews et al. (1972), for the simple location case].
Redescending \psi-functions are tricky, especially when the starting values for the iterations are non-robust. Residuals that are accidentally large because of the poor starting parameters then may stay large forever because they exert zero pull. It is therefore preferable to start with a monotone \psi, iterate to death, and then append a few (1 or 2) iterations with the nonmonotone \psi."