  Let $K$ be a local field with residue characteristic $p$ and let $L/K$ be a
totally ramified extension of degree $p^k$. In this paper we show that if $L/K$
has only two distinct indices of inseparability then there exists a uniformizer
$\pi_L$ for $L$ whose minimum polynomial over $K$ has at most three terms. This
leads to an explicit classification of extensions with two indices of
inseparability. Our classification extends work of Amano, who considered the
case $k=1$.
