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I will discuss a method to compute 1/N corrections in large N CFTs based on the Rayleigh-Schroedinger perturbation theory for the dilatation operator. I will apply the method to the simplest examples, i.e. subsectors of large-N CFTs defined by weakly coupled scalar fields in AdS. In particular, I will derive the 1/N^2 correction to the single-trace scaling dimension in phi^3 theories, and the 1/N^4 correction to the scaling dimension of (some) double-trace operators in phi^4 theories. When possible, I will compare with existing results obtained with other methods, and I will discuss the flat-space limit of the result.