The spectral resolution of broadband Fourier-transform coherent anti-Stokes Raman spectroscopy is limited by the maximum optical path length difference that can be scanned within a short time in an interferometer. However, alternatives to the Fourier transform exist which can bypass this limitation with certain assumptions. We apply one such approach to broadband coherent Raman spectroscopy using interferometers with a short delay line (low Fourier spectral resolution) and large delay line (high Fourier spectral resolution). With this method, we demonstrate that broadband coherent Raman spectroscopy of closely spaced vibrational bands is possible using a short delay line interferometer with comparable spectral resolution to the longer delay line instrument. We discuss how this approach may be particularly useful for more complex Raman spectra, such as those measured from biological samples.