  A conjecture of Breuil, Buzzard, and Emerton says that the slopes of certain
reducible $p$-adic Galois representations must be integers. In previous work we
showed this conjecture for representations that lie over certain non-subtle
components of weight space. This article is a continuation of that work in
which we completely classify the aforementioned representations over the
non-subtle components of weight space, both for integer and non-integer slopes.
