  Many standard model extensions, including composite Goldstone Higgs models,
predict vector-like fermionic top-partners at the TeV scale. The intensive
search programmes by ATLAS and CMS focus on decays into a 3$^{\rm rd}$
generation quark and an electroweak boson ($W,Z,h$). However, underlying models
of partial compositeness contain additional states that give rise to exotic top
partner decays. We consider a well-motivated scenario in which a charge-$2/3$
top-partner decays into a pseudo-scalar, $T\rightarrow t\ a$, with
$a\rightarrow gg \mbox{ or } b\bar{b}$ dominating below the $t\bar{t}$
threshold. We show that the constraints on the top partner mass from QCD pair
production are substantially weakened, still allowing a top partner mass as
light as $400$ GeV.
