  We prove that the Krull-Schmidt decomposition of the Galois module of the
$p$-adic completion of algebraic units is controlled by the primes that are
ramified in the Galois extension and the $S$-ideal class group. We also compute
explicit upper bounds for the number of possible Galois module structures of
algebraic units when the Galois group is cyclic of order $p^{2}$ or $p^{3}$.
