  Models of dark sectors with a mass threshold can have important cosmological
signatures. If, in the era prior to recombination, a relativistic species
becomes nonrelativistic and is then depopulated in equilibrium, there can be
measurable impacts on the cosmic microwave background as the entropy is
transferred to lighter relativistic particles. In particular, if this ``step''
occurs near $z\sim 20,000$, the model can naturally accommodate larger values
of $H_0$. If this stepped radiation is additionally coupled to dark matter,
there can be a meaningful impact on the matter power spectrum as dark matter
can be coupled via a species that becomes nonrelativistic and depleted. This
can naturally lead to suppressed power at scales inside the sound horizon
before the step, while leaving conventional cold dark matter signatures for
power outside the sound horizon. We study these effects and show such models
can naturally provide lower values of $S_8$ than scenarios without a step. This
suggests these models may provide an interesting framework to address the $S_8$
tension, both in concert with the $H_0$ tension and without.
