  Jet tagging has become an essential tool for new physics searches at the
high-energy frontier. For jets that contain energetic charged leptons we
introduce Feature Extended Supervised Tagging (FEST) which, in addition to jet
substructure, considers the features of the charged lepton within the jet. With
this method we build dedicated taggers to discriminate among boosted $H \to
\ell \nu q \bar q$, $t \to \ell \nu b$, and QCD jets (with $\ell$ an electron
or muon). The taggers have an impressive performance, allowing for overall
light jet rejection factors of $10^4-10^5$, for top quark / Higgs boson
efficiencies of $0.5$. The taggers are also excellent in the discrimination of
Higgs bosons from top quarks and vice versa, for example rejecting top quarks
by factors of $100-300$ for Higgs boson efficiencies of $0.5$. We demonstrate
the potential of these taggers to improve the sensitivity to new physics by
using as example a search for a new $Z'$ boson decaying into $Z H$, in the
fully-hadronic final state.
