Aspects of the tetrahedral neutrino mass matrix

The four-parameter tetrahedral neutrino mass matrix introduced earlier by the author is studied in two specific limits, both having only two parameters and resulting in theta(13)=0, theta(23)=pi/4, and tan(2)theta(12)=1/2. One limit corresponds to a recent proposal which predicts a normal ordering of neutrino masses; the other is new and allows both inverted and normal ordering.