  The Liouville integrability of the generalised type II defects is
investigated. Full integrability is not considered, only the existence of an
infinite number of conserved quantities associated with a system containing a
defect. For defects in affine Toda field theories (ATFTs) it is shown that
momentum conservation is very likely to be a necessary condition for
integrability. The defect Lax matrices which guarantee zero curvature, and so
an infinite number of conserved quantities, are calculated for the momentum
conserving Tzitz\'eica defect and the momentum conserving $D_4$ ATFT defect.
Some additional calculations pertaining to the $D_4$ defect are also carried
out to find a more complete set of defect potentials than has appeared
previously.
