We study the formal properties of extensions of the basic public announcement logic by standard modal axioms such as D, T, 2, 4, and 5. We show that some of them fail to be conservative extensions of the underlying modal logic. This leads us to propose new truth conditions for announcements that better suit these extensions. The corresponding reduction axioms postulate the suitability of the updated model to the underlying logic. We show that if the fact can be expressed that the frame of an updated model is in the class of frames of the underlying modal logic, then the public announcement extension is axiomatisable. This is the case for, for example, K, KT, S4, and S4.3. We also show that such a formula does not exist for several logics whose frame condition involves existential quantification. This is the case for, for example, S4.2