  We propose a method for determining the mass difference between two
particles, \slep_1 and \slep_2, that are nearly degenerate, with \Delta{m},
defined as m_2-m_1, being much less than m_1. This method applies when (a) the
\slep_1 momentum can be measured, (b) \slep_2 can only decay to \slep_1, and
(c) \slep_1 and \slep_2 can be produced in the decays of a common mother
particle. For small \Delta{m}, \slep_2 cannot be reconstructed directly,
because its decay products are too soft to be detected. Despite this, we show
that the existence of \slep_2 can be established by observing the shift in the
mother particle invariant-mass peak, when reconstructed from decays to \slep_2.
We show that measuring this shift would allow us to extract \Delta{m}. As an
example, we study supersymmetric gauge-gravity hybrid models in which \slep_1
is a meta-stable charged slepton next-to-lightest supersymmetric particle and
\slep_2 is the next-to-lightest slepton with \Delta{m} of about 5 GeV.
