  Let $U_l$ be a quantum group at an $l$th root of unity. Many tilting modules
for $U_l$ have been shown to have what we call a balanced semisimple
filtration, or a Loewy series whose semisimple layers are symmetric about some
middle layer. The existence of such filtrations suggests a remarkably
straightforward algorithm for calculating these characters if the irreducible
characters are already known. We first show that the results of this algorithm
agree with Soergel's character formula for the regular tilting modules. We then
show that these balanced semisimple filtrations really do exist for these
tilting modules.
