  We show that if $\mathcal{L}$ is a codimension-one lamination in a finite
volume hyperbolic 3-manifold such that the principal curvatures of each leaf of
$\mathcal{L}$ are all in the interval $(-\delta ,\delta)$ for a fixed
$\delta\in[0,1)$ and no complimentary region of $\mathcal{L}$ is an interval
bundle over a surface, then each boundary leaf of $\mathcal{L}$ has a
nontrivial fundamental group. We also prove existence of a fixed constant
$\delta_0 > 0$ such that if $\mathcal{L}$ is a codimension-one lamination in a
finite volume hyperbolic 3-manifold such that the principal curvatures of each
leaf of $\mathcal{L}$ are all in the interval $(-\delta_0 ,\delta_0)$ and no
complimentary region of $\mathcal{L}$ is an interval bundle over a surface,
then each boundary leaf of $\mathcal{L}$ has a noncyclic fundamental group.
