Corticomuscular coherence between the primary motor cortex (M1) and hand muscle electromyograms (EMG) occurs at approximately 20 Hz but is rarely seen at approximately 10 Hz. This is unexpected, because M1 has oscillations at both frequencies, which are effectively transmitted to the spinal cord via the corticospinal tract. We have previously speculated that a specific "neural filter" may selectively reduce coherence at approximately 10 Hz. This would have functional utility in minimizing physiological tremor, which often has a dominant component around this frequency. Recurrent inhibition via Renshaw cells in the spinal cord is a putative neural substrate for such a filter. Here we investigate this system in more detail with a biophysically based computational model. Renshaw cell recurrent inhibition reduced EMG oscillations at approximately 10 Hz, and also reduced corticomuscular coherence at this frequency (from 0.038 to 0.014). Renshaw cell inhibitory feedback also generated synchronous oscillations in the motoneuron pool at approximately 30 Hz. We show that the effects at 10 Hz and 30 Hz can both be understood from the dynamics of the inhibitory feedback loop. We conclude that recurrent inhibition certainly plays an important role in reducing 10 Hz oscillations in muscle, thereby decreasing tremor amplitude. However, our quantitative results suggest it is unlikely to be the only system for tremor reduction, and probably acts in concert with other neural circuits which remain to be elucidated.