Let $(M,\mathcal{F})$ be a regular smooth foliation on a manifold $M$. In general, the leaf space $M/\mathcal{F}$ is quite pathological. However, when $M$ is a Poisson manifold with compact, 1-connected leaves, the leaf space $M/\mathcal{F}$ is known to be a smooth manifold (cf. Poisson Manifolds of Compact Type 2 by Crainic, Fernandes and Martinez Torres).
I am wondering what conditions on the leaves should be put to make this work. Is it the compactness, the 1-connectedness or the combination of the two?