We have calculated the behavior of composite‐shell DT‐filled targets irradiated by constant‐power (’’unshaped’’) 1‐MeV electron beam pulses. The outer part of the shell (the ’’ablator’’) is composed of a lower‐Zmetal than the high‐density inner part (the ’’pusher’’). The lower‐Zablator decreases the bremsstrahlung heating of the pusher. The resulting colder and denser pusher is more effective. Breakeven requires about 360 TW deposited for 8 ns in a target about 3 mm in diameter. This is less than half the power required for targets composed of a single high‐density metal shell filled with DT.