Our two-dimensional (one velocity space and one spatial dimension), time- dependent model calculations indicate that an interplay between velocity and spatial diffusion may be responsible for the acceleration of implanted heavy ions in the cometary preshock region. Velocity diffusion (second-order Fermi acceleration) accelerates the pickup ions to moderate energies, thus creating a seed population for the more efficient diffusive-compressive shock acceleration. Solar wind convection limits the time available for diffusive- compressive acceleration, therefore the resulting energy spectrum above the pickup energy is a combination of an exponential decrease at lower energies (up to about 100 keV) and a power law spectrum at higher energies. The calculated energy spectra constitute a surprisingly good fit to the published VEGA and Giotto energy spectra above the pickup energy. ¿ American Geophysical Union 1989