  Stealth bosons are relatively light boosted particles with a cascade decay $S
\to A_1 A_2 \to q \bar q q \bar q$, reconstructed as a single fat jet. In this
work, we establish minimal extensions of the Standard Model that allow for such
processes. Namely, we consider models containing a new (leptophobic) neutral
gauge boson $Z'$ and two scalar singlets, plus extra matter required to cancel
the $\text{U}(1)'$ anomalies. Our analysis shows that, depending on the model
and benchmark scenario, the expected statistical significance of stealth boson
signals (yet uncovered by current searches at the Large Hadron Collider) is up
to nine times larger than for the most sensitive of the standard leptophobic
$Z'$ signals such as dijets, $t \bar t$ pairs or dibosons. These results
provide strong motivation for model-independent searches that cover these
complex signals.
