  We investigate exchange current contributions to elastic electron-deuteron
scattering using exactly Poincar\'e invariant quantum mechanics with a
null-plane kinematic symmetry. Our model exchange current is motivated by
one-pion-exchange physics. Exact current conservation and current covariance
are satisfied by using this current to compute a linearly independent set of
current matrix elements. The remaining current matrix elements are generated
from the independent matrix elements using the covariance and current
conservation constraints. The presence of the exchange current increases the
sensitivity to the choice of independent current matrix elements. Two choices
of independent matrix elements that have distinct motivations lead to a good
description of all of the elastic scattering observables for momentum transfers
below 8 (GeV)$^2$.
