  Electroweak precision measurements established that custodial symmetry is
preserved to a good accuracy in the gauge sector after electroweak symmetry
breaking. However, recent LHC results might be interpreted as pointing towards
Higgs couplings that do not respect such symmetry. Motivated by this
possibility, we reconsider the presence of an explicitly custodial breaking
coupling in a generic Higgs parameterization. After briefly commenting on the
large UV sensitivity of the T parameter to such a coupling, we perform a fit to
results of Higgs searches at LHC and Tevatron, and find that the apparent
enhancement of the ZZ channel with respect to WW can be accommodated. Two
degenerate best-fit points are present, which we label `Zphilic' and
`dysZphilic' depending on the sign of the hZZ coupling. Finally we highlight
some measurements at future linear colliders that may remove such degeneracy.
