  Let $X^o=\mathbb P^3\setminus D$ where $D$ is the union of two quadrics such
that their intersection contains a smooth conic, or the union of a smooth
quadric surface and two planes, or the union of a smooth cubic surface $V$ and
a plane $\Pi$ such that the intersection $V\cap\Pi$ contains a line. In all
these cases we show that the set of integral points of $X^o$ is potentially
dense. We apply the above results to prove that integral points are potentially
dense in some log-Fano or in some log-Calabi-Yau threefold.
