  While all models of Majorana neutrino masses lead to the same dimension five
effective operator, which does not conserve lepton number, the dimension six
operators induced at low energies conserve lepton number and differ depending
on the high energy model of new physics. We derive the low-energy dimension six
operators which are characteristic of generic Seesaw models, in which neutrino
masses result from the exchange of heavy fields which may be either fermionic
singlets, fermionic triplets or scalar triplets. The resulting operators may
lead to effects observable in the near future, if the coefficients of the
dimension five and six operators are decoupled along a certain pattern, which
turns out to be common to all models. The phenomenological consequences are
explored as well, including their contributions to $\mu \to e \gamma$ and new
bounds on the Yukawa couplings for each model.
