  We provide a nontrivial bound on the rank of any tensor $T$ over the
quaternions $\mathbb{H}$ in the $n_1\times n_2\times n_3$ cases where $2\leq
n_i\leq 3$. We describe a decomposition of $T$ into $3$ simple tensors in the
$2\times 2\times 2$ case. We also show that the upper bound is the best
possible for some of the cases, and we provide various partial results
involving tensor decompositions over $\mathbb{C}$ and $\mathbb{H}$.
