  We provide a complete classification up to isomorphism of all smooth convex
lattice 3-polytopes with at most 16 lattice points. There exist in total 103
different polytopes meeting these criteria. Of these, 99 are strict Cayley
polytopes and the remaining 4 are obtained as inverse stellar subdivisions of
such polytopes. We derive a classification, up to isomorphism, of all smooth
embeddings of toric threefolds in $\mathbb{P}^N$ where $N\le 15$. Again we have
in total 103 such embeddings. Of these, 99 are projective bundles embedded in
$\mathbb{P}^N$ and the remaining 4 are blow-ups of such toric threefolds.
