In observational radio astronomy, sideband-separating receivers are preferred, particularly under high atmospheric noise, which is usually the case in the sub-millimeter range. However, obtaining a good rejection ratio between the two sidebands is difficult since, unavoidably, imbalances in the different analog components appear. We describe a method to correct these imbalances without making any change in the analog part of the sideband-separating receiver, specifically, keeping the intermediate-frequency hybrid in place. This opens the possibility of implementing the method in any existing receiver. We have built hardware to demonstrate the validity of the method and tested it on a fully analog receiver operating between 600 and 720GHz. We have tested the stability of calibration and performance vs time and after full resets of the receiver. We have performed an error analysis to compare the digital compensation in two configurations of analog receivers, with and without intermediate frequency (IF) hybrid. An average compensated sideband rejection ratio of 46dB is obtained. Degradation of the compensated sideband rejection ratio on time and after several resets of the receiver is minimal. A receiver with an IF hybrid is more robust to systematic errors. Moreover, we have shown that the intrinsic random errors in calibration have the same impact for configuration without IF hybrid and for a configuration with IF hybrid with analog rejection ratio better than 10dB. Compensated rejection ratios above 40dB are obtained even in the presence of high analog rejection. The method is robust allowing its use under normal operational conditions at any telescope. We also demonstrate that a full analog receiver is more robust against systematic errors. Finally, the error bars associated to the compensated rejection ratio are almost independent of whether IF hybrid is present or not.