Quantitative analysis of optical coherence tomography data can be strongly hampered by speckle. Here, we introduce a new method to reduce speckle, which leverages from Fourier-domain configurations and operates on individual axial scans. By subdividing the digitized spectrum into a number of distinct narrower windows, each with a different center frequency, several independent speckle patterns result. These can be averaged to yield a lower-resolution image with strongly reduced speckle. The full resolution image remains available for human interpretation; the low resolution version can be used for parametric imaging or quantitative analysis. We demonstrate this technique using intravascular optical frequency domain imaging data acquired in vivo.