  We prove a generalization of Graham's Conjecture for optimal pebbling with
arbitrary sets of target distributions. We provide bounds on optimal pebbling
numbers of products of complete graphs and explicitly find optimal $t$-pebbling
numbers for specific such products. We obtain bounds on optimal pebbling
numbers of powers of the cycle $C_5$. Finally, we present explicit
distributions which provide asymptotic bounds on optimal pebbling numbers of
hypercubes.
