Approximate corrections for unresolved or slightly resolved sources with overestimated backgrounds. The model Gaussian source 𝒢 with a size of 10″ (FWHM) and a peak intensity of 1 is superposed on a flat background with a constant intensity of ℬ_0.9 = 0.6 (upper red lines). The increasingly overestimated backgrounds ℬ_0.7, ℬ_0.8, ℬ_0.9, ℬ_1.0, and ℬ_1.1 are shown with the dotted lines of different color. When such backgrounds are subtracted (lower colored curves), the source FWHM sizes A, peak intensities F_P, and total fluxes F_T become increasingly underestimated. The measured A values (given in the plot) get progressively smaller than the angular resolution of 10″, which clearly indicates an increasing inaccuracy of the background. Requiring that a source cannot be narrower than the telescope beam, it is possible to improve the measurements, substantially reducing their errors.