  In the Standard Model for electroweak interactions, the Higgs sector is known
to display a "custodial" symmetry protecting the mass relation
m_{W^\pm}^2=m_{W_3}^2 from large corrections. When considering extensions of
the scalar sector, this symmetry has to be introduced by hand in order to pass
current electroweak precision tests in a natural way. In this Letter we
implement a generalized custodial symmetry in the two-Higgs-doublet model.
Assuming the invariance of the potential under CP transformations, we prove the
existence of a new custodial scenario characterized by m_{H^\pm}^2=m_{H^0}^2
instead of m_{H^\pm}^2=m_{A^0}^2. Consequently the pseudoscalar A^0 may be much
lighter than the charged H^\pm, giving rise to interesting phenomenology.
