X-radiation may result from active plasma phenomena in the interactions of comets with the solar wind. We have carried out a limited but sensitive search for soft X-radiation from Comet Bradfield (1979l), on 1980 Feb. 5. No X-radiation was detected at a level (3σ) of 1.7 × 10-13 erg(cm2sec keV)-1 in the 0.2 - 4.0 kev range. This corresponds to a limit on the power dissipated in the comet by non-thermal electrons of approximately 1019 ergs sec-1, averaged over the 2568-sec exposure to the comet. This energy deposition is near the magnitude suggested by simple theoretical ideas, and further searches of appropriate comets both in soft X-radiation and at radio wavelengths seem warranted.