We numerically investigate high-power, modulational instability-based supercontinuum sources. Such sources have spectra that reach the infrared material absorption edge and as a result the spectrum has a strong narrow blue peak (dispersive wave group velocity matched to solitons at the infrared loss edge) followed by a significant dip in the neighboring longer-wavelength region. In a wide range of applications one prefers a broader and more flat blue part within a certain minimum and maximum power spectral density. From the perspective of fiber degradation it would be desirable to achieve this at reduced pump peak powers. We show that it is possible to improve the flatness by more than a factor of 3 by modulating the input peak power, although this comes at the expense of slightly higher relative intensity noise. Specifically, we consider a standard 6.6 W, 80 MHz supercontinuum source with a 455 nm blue edge, which uses 7 ps pump pulses. We then modulate its peak power to generate a pump pulse train having two and three different sub-pulses.