  In as-grown bulk crystals of Fe$_{1+y}$Te$_{1-x}$Se$_{x}$ with
$x\lesssim0.3$, excess Fe ($y>0$) is inevitable and correlates with a
suppression of superconductivity. At the same time, there remains the question
as to whether the character of the antiferromagnetic correlations associated
with the enhanced anion height above the Fe planes in Te-rich samples is
compatible with superconductivity. To test this, we have annealed as-grown
crystals with $x=0.1$ and 0.2 in Te vapor, effectively reducing the excess Fe
and inducing bulk superconductivity. Inelastic neutron scattering measurements
reveal low-energy magnetic excitations consistent with short-range correlations
of the double-stripe type; nevertheless, cooling into the superconducting state
results in a spin gap and a spin resonance, with the extra signal in the
resonance being short-range with a mixed single-stripe/double-stripe character,
which is different than other iron-based superconductors. The mixed magnetic
character of these superconducting samples does not appear to be trivially
explainable by inhomogeneity.
