  We provide new Schmidt-type results through an investigation of two
bijections, which are results involving partitions with parts counted only at
given indices. Mork's bijection, the first of these, was originally given as a
proof of Schmidt's theorem. We show that a version of Sylvester's bijection is
equivalent to Mork's bijection applied to 2-modular diagrams, which implies
refinements of existing results and new generating function identities. We then
develop a bijection based on an idea appearing in a recent paper of Andrews and
Keith, that places partitions counted at the indices $r$, $t+r$, $2t+r, \dots$
in correspondence with $t$-colored partitions. This leads to a substantial
generalization of an identity of Bridges and Uncu, and complements a similar
investigation of Li and Yee.
