  We consider conditions which force a well-quasi-ordered poset (wqo) to be
better-quasi-ordered (bqo). In particular we obtain that if a poset $P$ is wqo
and the set $S_{\omega}(P)$ of strictly increasing sequences of elements of $P$
is bqo under domination, then $P$ is bqo. As a consequence, we get the same
conclusion if $S_{\omega} (P)$ is replaced by $\mathcal J^1(P)$, the collection
of non-principal ideals of $P$, or by $AM(P)$, the collection of maximal
antichains of $P$ ordered by domination. It then follows that an interval order
which is wqo is in fact bqo.
