  This paper is a contribution to the growing investigation of strong
reducibilities between $\Pi^1_2$ statements of second-order arithmetic, viewed
as an extension of the traditional analysis of reverse mathematics. We answer
several questions of Hirschfeldt and Jockusch (to appear) about uniform and
strong computable reductions between various combinatorial principles related
to Ramsey's theorem for pairs. Among other results, we establish that the
principle $\mathsf{SRT}^2_2$ is not uniformly or strongly computably reducible
to $\mathsf{D}^2_{<\infty}$, that $\mathsf{COH}$ is not uniformly reducible to
$\mathsf{D}^2_{<\infty}$, and that $\mathsf{COH}$ is not strongly reducible to
$\mathsf{D}^2_2$. The latter also extends a prior result of Dzhafarov (2015).
We introduce a number of new techniques for controlling the combinatorial and
computability-theoretic properties of the problems and solutions we construct
in our arguments.
