  In this paper, we use Heegaard Floer homology to study reducible surgeries.
In particular, suppose K is a non-cable knot in the three-sphere with an
L-space surgery. If p-surgery on K is reducible, we show that p equals 2g(K)-1.
This implies that any knot with an L-space surgery has at most one reducible
surgery, a fact that we show additionally for any knot of genus at most two.
