  We investigate the impact of general conditions of theoretical stability and
cosmological viability on dynamical dark energy models. As a powerful example,
we study whether minimally coupled, single field Quintessence models that are
safe from ghost instabilities, can source the CPL expansion history recently
shown to be mildly favored by a combination of CMB (Planck) and Weak Lensing
(KiDS) data. We find that in their most conservative form, the theoretical
conditions impact the analysis in such a way that smooth single field
Quintessence becomes significantly disfavored with respect to the standard LCDM
cosmological model. This is due to the fact that these conditions cut a
significant portion of the (w0;wa) parameter space for CPL, in particular
eliminating the region that would be favored by weak lensing data. Within the
scenario of a smooth dynamical dark energy parametrized with CPL, weak lensing
data favors a region that would require multiple fields to ensure gravitational
stability.
