A compressible generalization of the Kraichnan model [Phys. Rev. Lett. 72,
1016 (1994)] of passive scalar advection is considered. The dynamical role
of compressibility on the intermittency of the scalar statistics is investi
gated for the direct cascade regime. Simple physical arguments suggest that
an enhanced intermittency should appear for increasing compressibility, du
e to the slowing down of Lagrangian trajectory separations. This is confirm
ed by a numerical study of the dependence of intermittency exponents on the
degree of compressibility, by a Lagrangian method for calculating simultan
eous N-point tracer correlations. [S1063-651X(99)51008-8].