This paper studies the impact of omission failures on asynchronous distributed s ystems with crash-stop failures. For the large group of problem specifications that are restricted to correct processes, we show how to transform a crash-stop related problem specification into an equivalent omission one. For that, we provide transformations for algorithms and failure detectors, such that if and only if an algorithm using a failure detector satisfies a problem specification, then the transformed algorithm using the transformed failure detector satisfies the transformed problem specification. Our transformed problem specification is ensured to be non-trivial, and moreover, the transformation reveals itself to be in a reasonable sense weakest failure detector preserving. Our results help to use the power of the well-understood crash-stop model to aut omatically derive solutions for the general omission model, which has recently raised interest for being noticeably applicable for security problems in distributed environments equipped with security modules such as smartcards.