We study estimation of factor models in a fixed-T panel data setting and significantly relax the common correlated effects (CCE) assumptions pioneered by Pesaran (2006) and used in dozens of papers since. In the simplest case, we model the unobserved factors as functions of the cross-sectional averages of the explanatory variables and show that this is implied by Pesaran's assumptions when the number of factors does not exceed the number of explanatory variables. Our approach allows discrete explanatory variables and flexible functional forms in the covariates. Plus, it extends to a framework that easily incorporates general functions of cross-sectional moments, in addition to heterogeneous intercepts and time trends. Our proposed estimators include Pesaran's pooled correlated common effects (CCEP) estimator as a special case. We also show that in the presence of heterogeneous slopes our estimator is consistent under assumptions much weaker than those previously used. We derive the fixed-T asymptotic normality of a general estimator and show how to adjust for estimation of the population moments in the factor loading equation.