Following the experimental characterization of the N,N-dimethylated uracil anion by Bowen and co-workers, we have undertaken an investigation of the influence of the methylation on the electron affinity of the uracil molecule. Both experiment and theory agree that, as it is in the case of the isolated uracil molecule, the methylated uracils can only attach excess electrons into diffuse dipole-bound states. The corresponding electron affinities are very small (several MeV). The bonding effect in the dipole-bound state depends on the magnitude of the molecular dipole and on the size of the molecule. Selective methylation of the uracil molecule can be used to reduce or increase the dipole value and to change the electron affinity of the molecule. The present calculated results are consistent with the experimental determination that N,N-dimethylation of uracil results in reduction of the electron affinity.