We present classical molecular dynamics simulations of the solvation dynamics of a strongly polar dye molecule in a weakly polar solvent. Solvation times and amplitudes are compatible with recent measurements. Several differences in the solvation dynamics relative to the widely studied case of strong polar solvents are exhibited: lesser importance of the inertial component of the Stokes shift, relaxation times close to individual solvent reorientational times, instead of the longitudinal relaxation time of the solvent, large amplitudes of translational and orientational relaxation over about 10 ps and the presence of a long-lived solvation shell in the excited state.