  We study the reverse mathematics and computability-the\-o\-re\-tic strength
of (stable) Ramsey's Theorem for pairs and the related principles COH and DNR.
We show that SRT$^2_2$ implies DNR over RCA$_0$ but COH does not, and answer a
question of Mileti by showing that every computable stable $2$-coloring of
pairs has an incomplete $\Delta^0_2$ infinite homogeneous set. We also give
some extensions of the latter result, and relate it to potential approaches to
showing that SRT$^2_2$ does not imply RT$^2_2$.
