very low-temperature calorimeters that use the entire unsuppressed sensor bandwidth (design rule 1), we will become directly sensitive to TES phase separation. Consequently we impose a second design constraint that $G_{tb} \ll G_{t \, int}$. As an added benefit, we think device operation and analysis will be significantly less complex, because we also naively expect that phase-separated TESs are highly sensitivity to position-dependent variations in $T_{c}$ and other thin-film properties that are likely culprits for at least some of the non-linearities that have been found when biasing CRESST devices [@Emilija_2008_thesis].

Expected CRESST Energy Resolution & Athermal Phonon Collection Efficiency  {#sec:PhononCollection}
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We have shown that the infinite bandwidth $\sigma_{Et}$ in Table \[tab:PhononEres\] significantly overestimates the athermal phonon energy sensitivity, since it does not account for the athermal phonon collection bandwidth, $\omega_{nt}$. Additionally, we must account for the fact that only a fraction $\epsilon_{nt}$ of the athermal phonons are collected in the TES, and thus a particle recoil in the absorber should be modeled as $$\begin{split}
    \frac{dP_{t}}{dE_{\gamma}} &= \frac{\epsilon_{nt}}{1+j\omega/\omega_{nt}}  \\
    \frac{dP_{a}}{dE_{\gamma}} &= 1-\epsilon_{nt}   
\end{split}
\label{eq:dIdExyz}$$ For an upper bound on $\epsilon_{nt}$, we note that optical photons directly incident on a W TES have been measured to deposit $\sim$ 42% of their 