An operation on an element container is said to provide a strong guarantee of exception safety if, in case an exception is thrown, the operation leaves the container in the state in which it was before the operation. In this paper, we explore how to adjust operations on C++ standard-library containers to provide the strong guarantee of exception safety, instead of the default guarantee, without violating the stringent performance requirements specified in the C++ standard. In particular, we show that every strongly exception-safe operation on dynamic arrays and ordered dictionaries is only a constant factor slower than the corresponding default-guarantee operation. In terms of the amount of space, the overhead introduced is linear in the number of elements stored.