Abstract: We discuss neutrino masses from higher than d = 5 effective operators in a supersymmetric framework, where we explicitly demonstrate which operators could be the leading contribution to neutrino mass in the minimal supersymmetric standard model and next to minimal supersymmetric standard model. As an example, we focus on the d = 7 operator LLH(u)H(u)H(d)H(u), for which we systematically derive all tree-level decompositions. We argue that many of these lead to a linear or inverse seesaw scenario with two extra neutral fermions, where the lepton number violating term is naturally suppressed by a heavy mass scale when the extra mediators are integrated out. We choose one example, for which we discuss possible implementations of the neutrino flavor structure. In addition, we show that the heavy mediators, in this case SU(2) doublet fermions, may indeed be observable at the LHC, since they can be produced by Drell-Yan processes and lead to displaced vertices when they decay. However, the direct observation of lepton number violating processes is on the edge at LHC.