We study the capacity regions of various broadband degraded broadcast channels including the degraded Poisson broadcast channel and the degraded very-noisy broadcast channel. It is shown that in the absence of dark current the capacity region of the degraded Poisson broadcast channel is achievable with a simple time-sharing strategy, and an analogous result is proved for the degraded very-noisy broadcast channel with binary inputs. Conditions are derived for time-sharing to be optimal for a general degraded very-noisy broadcast channel.