A codimension-1 foliation $\mathcal{F}$ of a (closed, connected, oriented) 3-manifold is taut if there exists a simple closed curve $\gamma$ that intersects each leaf of $\mathcal{F}$ transversely.

Using work of Thurston, you know that if a taut foliation has closed leaves, they must be homologically trivial. But how do you know when a taut foliation admits closed leaves at all? Is there some way to tell, or some class of manifolds which you know support a taut foliations with closed leaves?

Thanks!