  It is well-known that both the pathwidth and the outer-planarity of a graph
can be used to obtain lower bounds on the height of a planar straight-line
drawing of a graph. But both bounds fall short for some graphs. In this paper,
we consider two other parameters, the (simple) homotopy height and the (simple)
grid-major height. We discuss the relationship between them and to the other
parameters, and argue that they give lower bounds on the straight-line drawing
height that are never worse than the ones obtained from pathwidth and
outer-planarity.
