The Doppler spectrum of high-frequency radar echoes from the sea consists of dominant peaks due to first-order Bragg scatter surrounded by a higher-order continuum. Most applications to date have been based on the first-order lines, requiring multiple observations and large or moving antennas. In contrast, inversion of the second-order structure can yield the complete directional ocean wave spectrum from a single radar observation. In this report we describe the first inversion of measured second-order echo spectra from a 21.75-MHz narrow-beam radar looking in a single direction. Estimates of the directional ocean wave spectrum are compared with surface truth provided by tilt buoy and weather station, and fair agreement is found. This initial success is indicative of the potential of this technique for remote sensing of the sea surface.