Let D be a diagram of an alternating knot with unknotting number one. The branched double cover of S³ branched over D is an L-space obtained by half integral surgery on a knot K_D. We denote the set of all such knots K_D by $\mathcal D$. We characterize when K_D ∈ $\mathcal D$ is a torus knot, a satellite knot or a hyperbolic knot. In a different direction, we show that for a given n > 0, there are only finitely many L-space knots in $\mathcal D$ with genus less than n.

We would like to thank Ken Baker, Josh Greene, Matt Hedden, John Luecke and Tom Mark for helpful conversations. We are also grateful to an anonymous referee for their detailed feedback.