  Theories with gapped continuum spectra have gotten some attention, either as
pure 4D models like unparticles, or in 5D realizations as certain soft walls
constructions. In this paper, we derive experimental bounds from Drell-Yan
processes ($pp \to \ell^+\ell^-$, $pp \to \ell^\pm \nu$) in a particular
scenario where the electroweak bosons propagate in an extra dimension that
produces a propagator with a continuum spectrum, on top of the isolated
corresponding Standard Model pole. Using current LHC data we put a lower bound
on the gap of 4.2 TeV (expected), 6.2 TeV (observed, bins with $< 10$ events
combined) at 95\% CL, with some dependence in the observed limit on how low
statistics bins are treated. We also study the limits for HL-LHC.
