We investigate the problem of the predictability of random variable $Y$ under
a privacy constraint dictated by random variable $X$, correlated with $Y$,
where both predictability and privacy are assessed in terms of the minimum
mean-squared error (MMSE). Given that $X$ and $Y$ are connected via a
binary-input symmetric-output (BISO) channel, we derive the \emph{optimal}
random mapping $P_{Z|Y}$ such that the MMSE of $Y$ given $Z$ is minimized while
the MMSE of $X$ given $Z$ is greater than $(1-\epsilon)\mathsf{var}(X)$ for a
given $\epsilon\geq 0$. We also consider the case where $(X,Y)$ are continuous
and $P_{Z|Y}$ is restricted to be an additive noise channel.