Lucio's nickname for Mistress Overdone, "Madam Mitigation", references the bawd's ability to alleviate the sexual desires of her customers. However, ranging entries of the terms "mitigate" and "mitigation" in the Oxford English Dictionary add further dimension to Overdone's nickname.
Besides the more obvious definition, "To alleviate or give relief from (an illness or symptom, pain, suffering, sorrow, etc.)" another entry associates mitigation with "Compassion, mercy, or favour." This is particularly interesting in light of Shakespeare's careful juxtaposition of the main plot that occurs "above ground" and the subplot of the underworld. While the characters above ground (such as Angelo) undermine their outward concern for justice with deceitful and hypocritical actions, the characters of the underworld, though "dirty" and "diseased" prove altogether more honest and virtuous. Mistress Overdone, for example, demonstrates her maternal and generous nature by taking care of the baby of Lucio and one of her bawds. "I have kept it myself; and see how he goes about to abuse me!", she claims in 3.2, evidencing at once both her own compassion and Lucio's hypocrisy. It is due to this compassion, along with her honest conversations with Pompey, and her fear of "what will become of her" under stringent law, that Shakespeare manages to align the sympathies of his audience with a prostitute.
Another entry in the OED defines "mitigation" as "abatement or relaxation of the severity or rigour of a law, penalty, etc." This also seems relevant to Mistress Overdone's role in the play, as she embodies a group highly threatened by the strict and rigorous policies of Angelo and the Puritan pressure to rid the city of its vices. It is exactly "mitigation" she seeks from the authorities in response to her 'crimes': "Good my lord, be good to me", she begs Escalus in 3.2. It is again the positive light she is presented in (by her honest and compassionate nature) that causes the audience to also hope for the "relaxation of the severity or rigour of a law".
Perhaps the nickname, "Madam Mitigation", implies more than a prostitute's ability to please. Through the figure of Mistress Overdone, Shakespeare challenges a narrow representation of the urban underworld and acknowledges that even the most prominent embodiments of deviant sexuality may not necessarily be void of virtue.