  A profinite group G is just infinite if every non-trivial closed normal
subgroup of G is of finite index, and hereditarily just infinite if every open
subgroup is just infinite. Hereditarily just infinite profinite groups need not
be virtually pro-p, as shown in a recent paper of Wilson. The same paper gives
a criterion on an inverse system of finite groups that is sufficient to ensure
the limit is either virtually abelian or hereditarily just infinite. We give
criteria of a similar nature that characterise the just infinite and
hereditarily just infinite properties under the assumption that G is not
virtually pro-p.
