We discuss the connection between the origin of neutrino masses and their mixings which arises in a class of scenarios with radiatively induced neutrino masses. 
 In these scenarios, the neutrino mass matrix acquires textures with two entries close to zero in the basis where the charged-lepton mass matrix is diagonal. 
 This results in a specific pattern for the neutrino mixings, which leads to the prediction of (i) a Normal Hierarchy of the neutrino masses with the lightest 
 neutrino mass in the ~ meV range, (ii) testable correlations among the various mixing angles, including a non-zero ?13 angle with its exact value correlated with 
 the values of the atmospheric angle ?23 and the CP phase d. We quantify the impact of deviations from exact zeroes in the mass matrix texture, and connect it to 
 the amount of hierarchy among lepton masses. These scenarios of radiative neutrino mass generation also give rise to new short-range contributions to neutrinoless 
 double beta decay, which dominate over the usual light-neutrino exchange contribution. As a result, this class of models can have a sizable neutrinoless double beta 
 decay rate, in the range of upcoming experiments despite the normal mass hierarchy of neutrinos