  We consider how best to search for top partners in generic composite Higgs
models. We begin by classifying the possible group representations carried by
top partners in models with and without a custodial $SU(2)\times SU(2) \rtimes
\mathbb{Z}_2$ symmetry protecting the rate for $Z \rightarrow b\overline{b}$
decays. We identify a number of minimal models whose top partners only have
electric charges of $\frac{1}{3}, \frac{2}{3},$ or $\frac{4}{3}$ and thus decay
to top or bottom quarks via a single Higgs or electroweak gauge boson. We
develop an inclusive search for these based on a top veto, which we find to be
more effective than existing searches. Less minimal models feature light states
that can be sought in final states with like-sign leptons and so we find that 2
straightforward LHC searches give a reasonable coverage of the gamut of
composite Higgs models.
