The suppression of ring artifacts in x-ray computed tomography (CT) is a required step in practical applications; it can be addressed by introducing refined digital low pass filters within the reconstruction process. However, these filters may introduce additional ringing artifacts when simultaneously imaging pure phase objects and elements having a non-negligible absorption coefficient. Ringing originates at sharp interfaces, due to the truncation of spatial high frequencies, and severely affects qualitative and quantitative analysis of the reconstructed slices. In this work, we discuss the causes of ringing artifacts, and present a general compensation procedure to account for it. The proposed procedure has been tested with CT datasets of the mouse central nervous system acquired at different synchrotron radiation facilities. The results demonstrate that the proposed method compensates for ringing artifacts induced by low pass ring removal filters. The effectiveness of the ring suppression filters is not altered; the proposed method can thus be considered as a framework to improve the ring removal step, regardless of the specific filter adopted or the imaged sample.