It is known from earlier studies, that owing to enhanced radiation losses and dilution effects of the helium ash, the burn regime of ignited fusion plasmas in the neτE versus T plane has an upper limit when τE is the energy confinement time owing to heat conduction. So far no such upper limit has been found when radiation losses are included in the definition of τE. It is shown in this letter that an upper limit also exists in the latter case, and corresponding closed ignition curves are presented. Furthermore, it is shown that the operating regime of ignited plasma equilibria is restricted by a boundary of radiative equilibria that lies below the so-called radiation limit