  We compute $\tau_{RR}$ minimization in gauged supergravity for M-theory and
String Theory truncations with both massless and massive vector multiplets. We
explicitly compute, as anticipated in \cite{Amariti:2015ybz}, that massive
vector fields at the vacuum require the introduction of a constraint through a
Lagrange multiplier. We illustrate this explicitly in two examples, namely the
$U(1)^2$-invariant truncation dual to the mABJM model and the ISO(7) truncation
in massive IIA, the latter being a theory with both electric and magnetic
gauging. We revisit the vacuum constraints at $AdS_4$ and show how the
supergravity analysis matches the results of the field theory dual computation.
