  We combine the Twin Higgs mechanism with the paradigm of Composite Higgs
models. In this class of models the Higgs is a pseudo-Nambu-Goldstone boson
from a strongly coupled sector near the TeV scale, and it is additionally
protected by a discrete symmetry due to the twin mechanism. We discuss the
model building issues associated with this setup and quantify the tuning needed
to achieve the correct electroweak vacuum and the Higgs mass. In contrast to
standard Composite Higgs models, the lightest resonance associated with the top
sector is the uncolored mirror top, while the colored top partners can be made
parameterically heavier without extra tuning. In some cases, the vector
resonances are predicted to lie in the multi-TeV range. We present models where
the resonances - both fermions and vectors - being heavier alleviates the
pressure on naturalness coming from direct searches demonstrating that theories
with low tuning may survive constraints from the Large Hadron Collider.
