Glow discharges operated in narrow capillary tubes filled with helium, neon, or a mixture of both, feature strongly negative current-voltage characteristics at discharge currents of several mA and total pressures of a few Torr. These characteristics are computed assuming that the positive column, by virtue of wall-charge effects in the narrow tube, is not quasi-neutral, and hence the ion velocity directed towards the wall is greater than the mean thermal velocity. Measured and computed characteristics coincide remarkably well. The current and pressure range mentioned above should prove to be of substantial interest for He-Ne laser applications.