Models of dark sectors with a mass threshold can have important cosmological signatures. If, in the era prior to recombination, a relativistic species becomes non-relativistic and is then depopulated in equilibrium, there can be measurable impacts on the CMB as the entropy is transferred to lighter relativistic particles. In particular, if this ``step'' occurs near
, the model can naturally accommodate larger values of . 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 non-relativistic and depleted. This can naturally
lead to suppressed power at scales inside the sound horizon before the step,
while leaving conventional CDM signatures for power outside the sound horizon.
We study these effects and show such models can naturally provide lower values
of than scenarios without a step. This suggests these models may provide
an interesting framework to address the tension, both in concert with the
tension and without.