  We analyze the effects of spin-orbit coupling on fluctuations of the
conductance of a quantum dot fabricated in a GaAs heterostructure. We argue
that spin-orbit effects may become important in the presence of a large
parallel magnetic field B_{||}, even if they are negligble for B_{||}=0. This
should be manifest in the level repulsion of a closed dot, and in reduced
conductance fluctuations in dots with a small number of open channels in each
lead, for large B_{||}. Our picture is consistent with the experimental
observations of Folk et al.
