Rav Yosef was very reluctant to preside over rabbinical court cases – based on the statement of Chazal (Yevamos 109b) that a dayan (rabbinic judge) should always imagine that Gehinnom is open underneath him.
Once, two litigants brought a case of safek gezel (questionable theft) before him. When Rav Yosef understood that the case was only about the possibility of inadvertent theft, and that the litigants simply wanted to distance themselves from even the suspicion of wrongdoing, he agreed to hear their case.
First, he wrapped himself in his tallis (Choshen Mishpat, siman 8:2) and then he removed his glasses. He explained to the two litigants that, based on Chazal, it is forbidden to gaze at the face of a rasha (Megillah 28a) and also that, when the litigants stand before a judge, the judge should consider them reshaim (Avos 1:8). Thus cloaked in his tallis, he turned to the litigants and, instead of calling them by name, he called out, “Reuven and Shimon!” (the customary names used by Torah sources in illustrative examples). “Reuven and Shimon, what is the dispute between you? What is your question of possible theft?”
The litigants, upon seeing Rav Yosef considering their case with such gravity and awe, were so terrified that they quickly forgave each other for any inadvertent wrongdoing and fled in terror from his home! (Chemda Genuza, Vol. II, p.69)