  Fermionic top-partners arise in models such as Composite Higgs and Little
Higgs. They modify Higgs properties, in particular how the Higgs couples to top
quarks. Alas, there is a low-energy cancellation acting in the coupling of the
Higgs boson to gluons and photons. As a result of this cancellation, no
information about the spectrum and couplings of the top-partners can be
obtained in gluon fusion to Higgs, just the overall new physics scale. In this
paper we show that this is not the case when hard radiation is taken into
account. Indeed, differential distributions in Higgs plus jets are sensitive to
the top-partner mass and coupling to the Higgs. We exploit the transverse
momentum distribution of the hard jet to obtain limits on the top-partners in
the 14 TeV LHC run, finding that 300 ifb of data of 14 TeV LHC are sufficient
to rule out top-sector mixing angles $\sin^2 (\theta_R)$ > 0.05 for
top-partners with masses from 300 GeV to above 2 TeV.
