  We study the relationship between Donkin's Tilting Module Conjecture and
Donkin's Good $(p,r)$-Filtration Conjecture. Our main result was motivated by a
result of Kildetoft and Nakano showing that the Tilting Module Conjecture
implies one direction of the Good $(p,r)$-Filtration Conjecture. We observe
that the converse nearly holds; in particular a weaker version of the Good
$(p,r)$-Filtration Conjecture implies the Tilting Module Conjecture.
