  The hyperelliptic Torelli group is the subgroup of the mapping class group
consisting of elements that act trivially on the homology of the surface and
that also commute with some fixed hyperelliptic involution. We prove a Birman
exact sequence for hyperelliptic Torelli groups, and we show that this sequence
splits. As a consequence, we show that the hyperelliptic Torelli group is
generated by Dehn twists if and only if it is generated by reducible elements.
We also give an application to the kernel of the Burau representation.
