Dynamic analysis (instrumenting programs with code to detect and prevent errors during program execution) can be an effective approach to debugging, as well as an effective means to prevent harm being caused by malicious code. One problem with this approach is the runtime overhead introduced by the instrumentation. We define several techniques that involve using the results of static analysis to identify some cases where instrumentation can safely be removed. While we have designed the techniques with a specific dynamic analysis in mind (that used by the Runtime Type-Checking tool), the ideas may be of more general applicability.