  We show that density-weighted moments of the dissipation rate, $\epsilon_l$,
averaged over a scale $l$, in supersonic turbulence can be successfully
explained by the She and L\'ev\^eque model [Phys. Rev. Lett. {\bf 72}, 336
(1994)]. A general method is developed to measure the two parameters of the
model, $\gamma$ and $d$, based directly on their physical interpretations as
the scaling exponent of the dissipation rate in the most intermittent
structures ($\gamma$) and the dimension of the structures ($d$). We find that
the best-fit parameters ($\gamma=0.71$ and $d=1.90$) derived from the
$\epsilon_l$ scalings in a simulation of supersonic turbulence at Mach 6 agree
with their direct measurements, confirming the validity of the model in
supersonic turbulence.
