  Closed forms for $f_{\lambda,i} (q) := \sum_{\tau \in SYT(\lambda) :
des(\tau) = i} q^{maj(\tau)}$, the distribution of the major index over
standard Young tableaux of given shapes and specified number of descents, are
established for a large collection of $\lambda$ and $i$. Of particular interest
is the family that gives a positive answer to a question of Sagan and
collaborators. All formulas established in the paper are unimodal, most by a
result of Kirillov and Reshetikhin. Many can be identified as specializations
of Schur functions via the Jacobi-Trudi identities. If the number of arguments
is sufficiently large, it is shown that any finite principal specialization of
any Schur function $s_\lambda(1,q,q^2,\dots,q^{n-1})$ has a combinatorial
realization as the distribution of the major index over a given set of
tableaux.
