For three-phase AC-DC power conversion, the widely-used continuous current mode (CCM) modulation scheme results in relatively high semiconductor losses from hardswitching each device during half of the mains cycle. Triangular current mode (TCM) modulation, where the inductor current reverses polarity before turn-off, achieves zero-voltage-switching (ZVS) but at the expense of a wide switching frequency variation (15× for the three-phase design considered here), complicating filter design and compliance with EMI regulations. In this paper, we propose a new modulation scheme, sinusoidal triangular current mode (S-TCM), that achieves soft-switching, keeps the maximum switching frequency below the 150 kHz EMI regulatory band, and limits the switching frequency variation to only 3×. Under S-TCM, three specific modulation schemes are analyzed, and a loss-optimized weighting of the current bands across load is identified. The 2.2 kW S-TCM phase-leg hardware demonstrator achieves 99.7 % semiconductor efficiency, with the semiconductor losses accurately analytically estimated within 10 % (0.3 W). Relative to a CCM design, the required filter inductance is 6× lower, the inductor volume is 37 % smaller, and the semiconductor losses are 55 % smaller for a simultaneous improvement in power density and efficiency.