  We analyze the parametric structure of Twin Higgs (TH) theories and assess
the gain in fine tuning which they enable compared to extensions of the
Standard Model with colored top partners. Estimates show that, at least in the
simplest realizations of the TH idea, the separation between the mass of new
colored particles and the electroweak scale is controlled by the coupling
strength of the underlying UV theory, and that a parametric gain is achieved
only for strongly-coupled dynamics. Motivated by this consideration we focus on
one of these simple realizations, namely composite TH theories, and study how
well such constructions can reproduce electroweak precision data. The most
important effect of the Twin states is found to be the infrared contribution to
the Higgs quartic coupling, while direct corrections to electroweak observables
are sub-leading and negligible. We perform a careful fit to the electroweak
data including the leading-logarithmic corrections to the Higgs quartic up to
three loops. Our analysis shows that agreement with electroweak precision tests
can be achieved with only a moderate amount of tuning, in the range 5-10\%, in
theories where colored states have mass of order 3-5 TeV and are thus out of
reach of the LHC. For these levels of tuning, larger masses are excluded by a
perturbativity bound, which makes these theories possibly discoverable, hence
falsifiable, only at a future 100 TeV collider.
