  Let $\mathcal R$ be a $\Sigma^1_1$ binary relation, and recall that a set $A$
is $\mathcal R$-discrete if no two elements of $A$ are related by $\mathcal R$.
We show that in the Sacks and Miller forcing extensions of $L$ there is a
$\Delta^1_2$ maximal $\mathcal{R}$-discrete set. We use this to answer in the
negative the main question posed in \cite{Fischer2010} by showing that in the
Sacks and Miller extensions there is a $\Pi^1_1$ maximal orthogonal family
("mof") of Borel probability measures on Cantor space. By contrast, we show
that if there is a Mathias real over $L$ then there are no $\Sigma^1_2$ mofs.
