  We show that the reality conditions to be imposed on Ashtekar variables to
recover real gravity can be implemented as second class constraints a la Dirac.
Thus, counting gravitational degrees of freedom follows accordingly. Some
constraints of the real theory turn out to be non-polynomial, regardless of the
form, polynomial or non-polynomial, taken for the reality conditions. We
comment upon the compatibility of our approach with the recently proposed Wick
transform point of view, as well as on some alternatives for dealing with such
second class constraints.
