We develop a technique for optimizing the phase of broad spectrally-separated frequency sidebands-a "holey" spectrum. We use a source of multiple-order coherent Raman sidebands, obtained by crossing femtosecond pump and Stokes beams in synthetic single-crystal diamond. We combine the sidebands into a single beam and show the phase coherence among the sidebands by investigating the interference between them in groups of three while varying one sideband phase by an acousto-optics pulse shaper. We then show how we optimize the broad "holey" spectrum by overcoming the limited temporal shaping window of the pulse shaper. We also explore how the resultant second harmonic/sum frequency generation of the full combined broadband spectrum varies as we vary different sideband phases. This step-by-step phase optimization of the "holey" spectrum can be applied to sidebands with similar structure to synthesize arbitrary optical waveforms.