  Planar posets can have arbitrarily large dimension. However, a planar poset
of height $h$ has dimension at most $192h+96$, while a planar poset with $t$
minimal elements has dimension at most $2t+1$. In particular, a planar poset
with a unique minimal element has dimension at most $3$. In this paper, we
extend this result by showing that a planar poset has dimension at most $6$ if
it has a plane diagram in which every minimal element is accessible from below.
