  We study phase segregation in a model alloy undergoing both ordering and
decomposition, using computer simulations of Kawasaki exchange dynamics on a
square lattice. Following a quench into the miscibility gap we observe an early
stage in which ordering develops while the composition remains almost uniform.
Then decomposition starts with segregation into ordered and disordered phases.
The two spherically averaged structure functions, related to decomposition and
to ordering, were both observed to obey scaling rules in the late coarsening
stage where the time increase of the characteristic lengths was consistent with
$a(t^{1/3} + b)$. While $a$ was similar for ordering and decomposition at low
concentration of the minority component, it showed an increase (decrease) with
concentration for ordering (decomposition). The domain morphology was found to
depend on the concentration of the minority component, in a way that suggests a
wetting of antiphase boundaries in the ordered domains by the disordered phase.
