Among the existing estimators of factor-augmented regressions, the CCE approach is the most popular. A major reason for this popularity is the simplicity and good small-sample performance of the approach, making it very attractive from an empirical point of view. The main drawback is that most of the available asymptotic theory is based on quite restrictive assumptions, such as that the common factor component should be independent of the regressors. The present paper can be seen as a reaction to this. The purpose is to study the asymptotic properties of the pooled CCE estimator under more realistic conditions. In particular, the common factor component may be correlated with the regressors, and the true number of common factors, r, can be larger than the number of estimated factors, which in CCE is given by k+1, where k is the number of regressors. The main conclusion is that while the estimator is generally consistent, asymptotic normality can fail when r>k+1.