The dependence of the measured radiation losses in ETA-BETA II on plasma density and plasma current rise time is discussed. A high-density limit is found, corresponding to large radiation. Above this limit, burning through the light impurities (mainly oxygen) does not take place and a cold, radiation-dominated discharge is obtained. This high-density limit scales with the plasma current, indicating a lower limit on the I/N parameter similar to the tokamak high-density limit. With longer current rise times the radiation energy loss during the set-up phase increases about linearly with rise time, corresponding always to about 50% of the total energy losses during this phase.