We characterize models where electroweak symmetry breaking is driven by two light Higgs doublets arising as pseudo-Nambu-Goldstone bosons of new dynamics above the weak scale. They represent the simplest natural two Higgs doublet alternative to supersymmetry. We construct their low-energy effective Lagrangian making only few specific assumptions about the strong sector. These concern their global symmetries, their patterns of spontaneous breaking and the sources of explicit breaking. In particular we assume that all the explicit breaking is associated with the couplings of the strong sector to the Standard determined at lowest order by very few free parameters associated to the top sector. Another crucial property of our scenarios is the presence of a discrete symmetry, in addition to custodial SO(4), that controls Model fields, that is gauge and (proto)-Yukawa interactions. Under those assumptions the scalar potential is the T-parameter. That can either be simple CP or a Z(2) that distinguishes the two Higgs doublets. Among various possibilities we study in detail models based on SO(6)/S0(4) x SO(2), focussing on their predictions for the structure of the scalar spectrum and the deviations of their couplings from those of a generic renormalizable two Higgs doublet model. (C) 2011 Elsevier B.V. All rights reserved.