Belief revision and update, two significant types of belief change, both focus on how an agent modifies her beliefs in presence of new information. The most striking difference between them is that the former studies the change of beliefs in a static world while the latter concentrates on a dynamically-changing world. The famous AGM and KM postulates were proposed to capture rational belief revision and update, respectively. However, both of them are too permissive to exclude some unreasonable changes in the iteration. In response to this weakness, the DP postulates and its extensions for iterated belief revision were presented. Furthermore, Ferme and Goncalves integrated these postulates in belief update. Unfortunately, some redundant components are included in the definitions of belief states and the faithful assignments for semantic characterizations. Moreover, their approach does not meet the desired property of iterated belief update. They also do not discuss the rationale of any DP postulate within the update context. This paper is intended to fix these deficiencies of Ferme and Goncalves’s approach. Firstly, we present a modification of the original KM postulates based on belief states, and propose the notion of faithful collective assignments of belief states to partial preorders. Subsequently, we migrate several well-known postulates for iterated belief revision to iterated belief update. Moreover, we provide the exact semantic characterizations based on partial preorders for each of the proposed postulates. Finally, we analyze the compatibility between the above iterated postulates and the KM postulates for belief update.