Capability machines are a type of CPUs that support fine-grained privilege separation using capabilities, machine words that include forms of authority. Formal models of capability machines and associated calling conventions have so far focused on establishing two forms of stack safety properties, namely local state encapsulation and well-bracketed control flow. We introduce a novel kind of directed capabilities and show how to use them to make an earlier suggested calling convention more efficient. In contrast to earlier work on capability machine models we do not only consider integrity properties but also confidentiality properties; we provide a unary logical relation to reason about the former and a binary logical relation to reason about the latter, each expressive enough to reason about temporal stack safety. While the logical relations are useful for reasoning about concrete examples, they do not on their own demonstrate that stack safety holds for a large class of programs. Therefore, we also show full abstraction of a compiler from an overlay semantics that internalizes the calling convention as a single call step and explicitly keeps track of the call stack and frame lifetimes to a base capability machine. All results have been mechanized in Coq