Envelope-tracking marching-on-in-time (ET-MOT) solution of the combined-field integral equation is compared to its traditional time-domain (TD) counterpart. ET techniques are generally more efficient than TD ones for band-pass scattering analysis because they can use larger time-step sizes that are constrained by the bandwidth rather than the maximum frequency component of the fields/currents. Yet, complexity analysis and numerical results show that the ET-MOT marching cost is proportional to the (relative) bandwidth only for low-frequency regime of analysis and that it is not a monotonic function of the bandwidth in general.