Systems-of-systems are formed by the composition of independently created software components into a single system. These participating components are designed to satisfy their own requirements, and may not satisfy the overall requirements of the system-of-systems. We refer to components that cannot be adapted to meet both individual and global requirements as “defiant” components. We propose a “cautious” adaptation approach that supports changing the behaviour of such defiant components under exceptional conditions to satisfy global requirements, while continuing to guarantee the satisfaction of the components’ individual requirements. The approach uses scenarios to represent normal and exceptional conditions; models the behaviour of exceptional conditions as wrappers implemented using an aspect-oriented technique; and adapts accordingly at runtime. We consider both single and multiple defiant components, with several instances of these components operating at the same time. We evaluated the implementation of our approach using an organ delivery drone application, conceived by our industrial partners, the results of which are presented and discussed in the paper.