A long-spacing velocity log contains almost the same information as an ideal short-spacing log, but in a distorted form with added noise. The distortion can be thought of as a moving average or smoothing filter. Its inverse, called a "sharpening" filter by astronomers, amplifies noise. If the inverse is to be useful, it must be designed with a balance between errors due to noise amplification and those due to incomplete sharpening. The Wiener optimum filter theory gives a prescription for achieving this balance. The result is called an optimum inverse filter. We have calculated finite-memory optimum inverse filters using the IBM 704. We have applied them to actual data, digitized in the field, to produce synthetic short-spacing velocity logs. These we have compared with their field counterparts. The synthetic logs have less calibration error and are free from noise spikes. The general agreement is good.