  Composite Higgs Models are often constructed including fermionic top partners
with a mass around the TeV scale, with the top partners playing the role of
stabilizing the Higgs potential and enforcing partial compositeness for the top
quark. A class of models of this kind can be formulated in terms of fermionic
strongly coupled gauge theories. A common feature they all share is the
presence of specific additional scalar resonances, namely two neutral singlets
and a colored octet, described by a simple effective Lagrangian. We study the
phenomenology of these scalars, both in a model independent and model dependent
way, including the bounds from all the available searches in the relevant
channels with di-boson and di-top final states. We develop a generic framework
which can be used to constrain any model containing pseudo-scalar singlets or
octets. Using it, we find that such signatures provide strong bounds on the
compositeness scale complementary to the traditional EWPT and Higgs couplings
deviations. In many cases a relatively light scalar can be on the verge of
discovery as a first sign of new physics.
