  In their simplest form, metric-like Lagrangians for higher-spin massless
fields display constrained gauge symmetries, unless auxiliary fields are
introduced or locality is foregone. Specifically, in its standard incarnation,
gauge invariance of Maxwell-like Lagrangians relies on parameters with
vanishing divergence. We propose an alternative form of the corresponding local
symmetry involving unconstrained parameters of mixed-symmetry type, described
by rectangular two-row Young diagrams and entering high-derivative gauge
transformations. The resulting gauge algebra appears to be reducible and we
display the full pattern of gauge-for-gauge parameters, testing its correctness
via the corresponding counting of degrees of freedom. Incidentally, this shows
that massless higher spins admit a local unconstrained formulation with no need
for auxiliary fields.
