A Standard-Model-like Higgs boson should be light in order to comply with electroweak precision measurements from LEP. We consider five-dimensional (5D) warped models -- with a deformation of the metric in the IR region -- as UV completions of the Standard Model with a heavy Higgs boson. Provided the Higgs boson propagates in the 5D bulk the Kaluza Klein (KK) modes of the gauge bosons can compensate for the Higgs boson contribution to oblique parameters while their masses lie within the range of the LHC. The little hierarchy between KK scale and Higgs mass essentially disappears and the naturalness of the model greatly improves with respect to the AdS (Randall-Sundrum) model. In fact the fine-tuning is better than 10% for all values of the Higgs boson mass.