  The modules $A_\mathfrak{q}(\lambda)$ of $U(p,q)$ can be parameterized by
their annihilators and asymptotic supports, both of which can be identified
using Young tableaux. Trapa developed an algorithm for determining the tableaux
of the modules $A_\mathfrak{q}(\lambda)$ in the mediocre range, along with an
equivalent condition to determine non-vanishing. The condition involves a
combinatorial concept called the overlap, which is not straightforward to
compute. In this paper, we establish a formula for the overlap and simplify the
condition for ease of use. We then apply it to $K$-types and the Dirac index of
$A_\mathfrak{q}(\lambda)$.
