  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
Model fields, that is gauge and (proto)-Yukawa interactions. Under those
assumptions the scalar potential is 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 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)/SO(4)$\times$ 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.
