  Long-lived alpha and beta emitters in the $^{222}$Rn decay chain on (and
near) detector surfaces may be the limiting background in many experiments
attempting to detect dark matter or neutrinoless double-beta decay, and in
screening detectors. In order to reduce backgrounds from radon-daughter
plate-out onto the wires of the BetaCage during its assembly, an
ultra-low-radon cleanroom is being commissioned at Syracuse University using a
vacuum-swing-adsorption radon-mitigation system. The radon filter shows
~20$\times$ reduction at its output, from 7.47$\pm$0.56 to 0.37$\pm$0.12
Bq/m$^3$, and the cleanroom radon activity meets project requirements, with a
lowest achieved value consistent with that of the filter, and levels
consistently < 2 Bq/m$^3$.
