The paper aims at making a contribution to the axiomatic approach to subjective uncertainty by introducing a modified set of six axioms to subjective probabilities. Those are considered sufficient to guarantee adequacy and rationality in the expression of beliefs in future uncertain events by the observer of the system. The axioms combine mathematical correctness and unambiguous justification. They draw on existing axiomatic bases, but include some additional features and dependencies. A modified theorem for existence and uniqueness of subjective probabilities that uses the axioms discussed is also stated in the paper, and some explanation is given regarding the way to acquire its strict mathematical justification.