Output power versus current characteristics of a multiple-anode hollow-cathode He-I2 laser have been studied using Quasicontinuous excitation. Oscillation has been obtained on a total of 25 transitions of I+ ranging in wavelength from the blue to near infrared and including 9 new CW transitions. For all transitions, upper level excitation is attributed to thermal-energy charge-transfer reactions. No saturation in laser output power has been detected for increasing discharge current up to 20 A in the 75-cm-long 2.5-mm-bore device. CW power levels up to 100 mW each for strong transitions and approaching 1W total over all transitions have been achieved.