  We present a general solution to the long standing problem of determining the
masses of pair-produced, semi-invisibly decaying particles at hadron colliders.
We define two new transverse kinematic variables, $M_{CT_\perp}$ and
$M_{CT_\parallel}$, which are suitable one-dimensional projections of the
contransverse mass $M_{CT}$. We derive analytical formulas for the boundaries
of the kinematically allowed regions in the $(M_{CT_\perp},M_{CT_\parallel})$
and $(M_{CT_\perp},M_{CT})$ parameter planes, and introduce suitable variables
$D_{CT_\parallel}$ and $D_{CT}$ to measure the distance to those boundaries on
an event per event basis. We show that the masses can be reliably extracted
from the endpoint measurements of $M_{CT_\perp}^{max}$ and $D_{CT}^{min}$ (or
$D_{CT_\parallel}^{min}$). We illustrate our method with dilepton $t\bar{t}$
events at the LHC.
