  We study the way a strongly irreducible Heegaard surface $\Sigma$ intersects
a knot exterior $X$ embedded in a 3-manifold, and show that if $\Sigma \cap
\partial X$ consists of simple closed curves which are essential in both
$\Sigma$ and $\partial X$, then the intersection $X \cap \Sigma$ consists of
meridional annuli only. As an application we show that when considering two
Heegaard surfaces that intersect essentially and spinally (cf. Rubinstein and
Shcarlemann) any embedded torus in the union of the two bounds a solid torus.
