  Given two Clark-Aleksandrov measures $\sigma^1$ and $\sigma^2$ on $\bT^2$, we
prove a theorem relating the property that $\sigma^1 \ll \sigma^2$ to
containment of a concrete function in a certain de Branges-Rovnyak space. We
show that our theorem is applicable for all rational inner functions on
$\bD^2$, and we provide several examples of how the theorem can be applied to
investigate Clark-Aleksandrov measures related to such functions.
