  Much work has been done recently towards trying to understand the topological
significance of being an L-space. Building on work of Rasmussen and Rasmussen,
we give a topological characterisation of Floer simple manifolds such that all
non-longitudinal fillings are L-spaces. We use this to partially classify
L-space twisted torus knots in $S^1 \times S^2$ and resolve a question asked by
Rasmussen and Rasmussen.
