  We improve the bound on the number of tetrahedra in the veering triangulation
of a fully-punctured pseudo-Anosov mapping torus in terms of the normalized
dilatation. When the mapping torus has only one boundary component, we employ
various techniques to improve the bound further. Together with the author's
work with Hironaka in the case when the mapping torus has at least two boundary
components, this allows us to understand small elements of the set
$\mathcal{D}$ of normalized dilatations of fully-punctured pseudo-Anosov maps
using computational means. In particular, we certify that the minimum element
of $\mathcal{D}$ is $\mu^2$ and the minimum accumulation point of $\mathcal{D}$
is $\mu^4$, where $\mu = \frac{1 + \sqrt{5}}{2} \approx 1.618$ is the golden
ratio.
