  We advocate the use of on-shell constrained $M_2$ variables in order to
mitigate the combinatorial problem in SUSY-like events with two invisible
particles at the LHC. We show that in comparison to other approaches in the
literature, the constrained $M_2$ variables provide superior ansatze for the
unmeasured invisible momenta and therefore can be usefully applied to
discriminate combinatorial ambiguities. We illustrate our procedure with the
example of dilepton $t\bar{t}$ events. We critically review the existing
methods based on the Cambridge $M_{T2}$ variable and MAOS-reconstruction of
invisible momenta, and show that their algorithm can be simplified without loss
of sensitivity, due to a perfect correlation between events with complex
solutions for the invisible momenta and events exhibiting a kinematic endpoint
violation. Then we demonstrate that the efficiency for selecting the correct
partition is further improved by utilizing the $M_2$ variables instead.
Finally, we also consider the general case when the underlying mass spectrum is
unknown, and no kinematic endpoint information is available.
