Human corticospinal transmission is commonly studied using brain stimulation. However, this approach is biased to activity in the fastest conducting axons. It is unclear whether conclusions obtained in this context are representative of volitional activity in mild-to-moderate contractions. An alternative to overcome this limitation may be to study the corticospinal transmission of endogenously generated brain activity. Here we investigate in humans (N=19; of either sex), the transmission speeds of cortical beta rhythms (∼20Hz) traveling to arm (first dorsal interosseous) and leg (tibialis anterior) muscles during tonic mild contractions. For this purpose, we propose two improvements for the estimation of cortico-muscular beta transmission delays. First, we show that the cumulant density (cross-covariance) is more accurate than the commonly-used directed coherence to estimate transmission delays in bidirectional systems transmitting band-limited signals. Second, we show that when spiking motor unit activity...