The discovery of extraordinary optical transmission (EOT) through patterned metallic foils in the late 1990s was decisive for the development of plasmonics and cleared the path to employ small apertures for a variety of interesting applications all along the electromagnetic spectrum. However, a typical drawback often found in practical EOT structures is the large size needed to obtain high transmittance peaks. Consequently, practical EOT arrays are usually illuminated using an expanded (mimicking a plane wave) beam. Here, it is shown with numerical and experimental results in the THz range that high transmittance peaks can be obtained even with a reduced illumination spot exciting a small number of holes, provided that the structure has a sufficient number of lateral holes out of the illumination spot. These results shed more light on the prominent role of leaky waves in the underlying physics of EOT and have a direct impact on potential applications.