  The cosmic microwave background (CMB) places a variety of model-independent
constraints on the strength interactions of the dominant component of dark
matter with the Standard Model. Percent-level subcomponents of the dark matter
can evade the most stringent CMB bounds by mimicking the behavior of baryons,
allowing for larger couplings and novel experimental signatures. However, in
this note, we will show that such tightly coupled subcomponents leave a
measurable imprint on the CMB that is well approximated by a change to the
helium fraction, $Y_{\rm He}$. Using the existing constraint on $Y_{\rm He}$,
we derive a new upper limit on the fraction of tightly coupled dark matter,
$f_{\rm TCDM}$, of $f_{\rm TCDM}<0.006$ (95\% C.I.). We show that future CMB
experiments can reach $f_{\rm TCDM}<0.001$ (95\% C.I.) and confirm that the
bounds derived in this way agree with the results of a complete analysis. We
briefly comment on the implications for model building, including milli-charged
dark matter.
