  We show how to parameterise solutions of the general relativistic vector
constraint equation on Einstein manifolds by unconstrained potentials. We
provide a similar construction for the trace-free part of tensors satisfying
the linearised scalar constraint. Previous work of ours has provided similar
different constructions for solutions of the linearized constraints in the case
where the cosmological constant $\Lambda$ is zero. We use our new potentials to
show that one can shield linearised gravitational fields using linearised
gravitational fields without imposing the TT gauge (as done in previous work),
for any value of $\Lambda \in \mathbb{R}$.
