  This document describes some special cases in which the stransverse mass,
MT2, may be calculated by non-iterative algorithms. The most notable special
case is that in which the visible particles and the hypothesised invisible
particles are massless -- a situation relevant to its current usage in the
Large Hadron Collider as a discovery variable, and a situation for which no
analytic answer was previously known. We also derive an expression for MT2 in
another set of new (though arguably less interesting) special cases in which
the missing transverse momentum must point parallel or anti parallel to the
visible momentum sum. In addition, we find new derivations for already known
MT2 solutions in a manner that maintains manifest contralinear boost invariance
throughout, providing new insights into old results. Along the way, we stumble
across some unexpected results and make conjectures relating to geometric forms
of M_eff and H_T and their relationship to MT2.
