Low rate coders based on the harmonic-noise model are sensitive to acoustic background noise at low SNRs due to the increase in parameter errors from the analysis of noisy speech. We investigate the use of spectral subtraction enhancement preprocessing on the performance of the sinusoidal model based codec both by objective assessment of parameter errors and the subjective testing of output speech quality and intelligibility. We find that while for noisy speech enhancement, improving speech quality is often accompanied by a decrease in intelligibility, in the context of coding, significant combined improvements are obtained when the speech coder is combined with a speech enhancement preprocessor.