We construct a simple theory in which the fine-tuning of the standard model is significantly reduced. Radiative corrections to the quadratic part of the scalar potential are constrained to be symmetric under a global U(4) x U(4){prime} symmetry due to a discrete Z{sub 2} 'twin' parity, while the quartic part does not possess this symmetry. As a consequence, when the global symmetry is broken the Higgs fields emerge as light pseudo-Goldstone bosons, but with sizable quartic self-interactions. This structure allows the cutoff scale, {Lambda}, to be raised to the multi-TeV region without significant fine-tuning. In the minimal version of the theory, the amount of fine-tuning is about 15% for {Lambda} = 5 TeV, while it is about 30% in an extend...