  We compute two parametric determinants in which rows and columns are indexed
by compositions, where in one determinant the entries are products of binomial
coefficients, while in the other the entries are products of powers. These
results generalize previous determinant evaluations due to the first and third
author [SIAM J. Matrix Anal. Appl. 23 (2001), 459--471] and ["A polynomial
generalization of the power-compositions determinant," Linear Multilinear
Algebra (to appear)], and they prove two conjectures of the second author
["Advanced determinant calculus: a complement," preliminary version].
