  Is the weak scale natural? This ever pending question makes the search for
new particle production a highly motivated primary goal of the next LHC phase.
These searches may or may not be successful. While waiting for a needed higher
energy collider to extend the direct exploration, the search for signs of new
physics might be confined to indirect tests for quite some time. In a few fully
calculable models, weakly or semi-strongly interacting, we compare the
significance to measure the Higgs couplings versus the electroweak observables.
