Using a one-dimensional hydrodynamic code we have simulated the radial evolution of heliospheric disturbances produced by slow coronal mass ejections (CMEs) embedded in much faster leading and trailing ambient solar wind. We find that pressure gradients induced by initial speed differences between slow CMEs and faster ambient wind can produce large accelerations of the CMEs, eventually nearly up to the speed of the ambient wind. The compressions, rarefactions, and shocks associated with this acceleration persist to large heliocentric distances. Comparison with observations reveals that such effects helped accelerate two of the six-high-latitude, CME events observed by Ulysses. ¿ American Geophysical Union 1996