  This paper compares notions of double sliceness for links. The main result is
to show that a large family of 2-component Montesinos links are not strongly
doubly slice despite being weakly doubly slice and having doubly slice
components. Our principal obstruction to strong double slicing comes by
considering branched double covers. To this end we prove a result classifying
Seifert fibered spaces which admit a smooth embeddings into integer homology
$S^1 \times S^3$s by maps inducing surjections on the first homology group. A
number of other results and examples pertaining to doubly slice links are also
given.
