Breakdown measurements for a small cylindrical cathode in an atmospheric-pressure flowing plasma of variable ionization (between 1015 and 1018 m−3) are reported for both DC voltages and fast-rise pulses (rise time 0·16 μs) applied to the cathode. For these measurements the breakdown voltages are found to be reduced to as little as fraction one-sixth of the breakdown voltage with no ionization. The measurements agree reasonably well with a theoretical model in which the anode is not the positive electrode in the plasma, but rather the edge of the coaxial sheath which surrounds the cathode, with breakdown voltages being given by the well-known breakdown relation for coaxial gaps. (For cylindrical geometry and a thick sheath, the ion space charge in the sheath is shown not to change materially the electric field from its value calculated for a conventional coaxial gap of the same dimensions.) In this experiment the impedance of the plasma between the sheath edge and the actual positive electrode is low enough for breakdown not to occur over this region. It is expected that this model will be used to predict reignition voltages at short recovery times in circuit breakers.