  For a hyperbolic knot in $S^3$, Dehn surgery along slope $r \in \Q \cup
\{\frac10\}$ is {\em exceptional} if it results in a non-hyperbolic manifold.
We say meridional surgery, $r = \frac10$, is {\em trivial} as it recovers the
manifold $S^3$. We provide evidence in support of two conjectures. The first
(inspired by a question of Professor Motegi) states that there are boundary
slopes $b_1 < b_2$ such that all non-trivial exceptional surgeries occur, as
rational numbers, in the interval $[b_1,b_2]$. We say a boundary slope is {\em
NIT} if it is non-integral or toroidal. Second, when there are non-trivial
exceptional surgeries, we conjecture there are NIT boundary slopes $b_1 \leq
b_2$ so that the exceptional surgeries lie in $[\floor{b_1},\ceil{b_2}]$.
Moreover, if $\ceil{b_1} \leq \floor{b_2}$, the integers in the interval $[
\ceil{b_1}, \floor{b_2} ]$ are all exceptional surgeries.
