The phrase "not worth a damn" is a derogatory expression that denotes the lack of value or importance of something or someone. However, there are several synonyms that can be used in its place, depending on the context and tone of the statement. Some alternatives to consider are "worthless," "useless," "pointless," "meaningless," "incompetent," "ineffective," and "unproductive." Other options may include "worthless," "unworthy," "trivial," and "insignificant." Choosing the appropriate synonym can add nuance and depth to a statement, expressing the speaker's attitude towards the topic more precisely.