An apparatus and method are provided for controlling use of bounded pointers. The apparatus has a plurality of bounded pointer storage elements, each bounded pointer storage element being used to store a bounded pointer and associated permission attributes indicative of allowed uses of the bounded pointer. In accordance with the present technique, the associated permission attributes include a copy permission attribute indicating whether the bounded pointer is allowed to be subjected to a copy operation. Processing circuitry is then responsive to at least one instruction that specifies the copy operation, to generate, from a source bounded pointer and associated permission attributes of a source bounded pointer storage element, a destination bounded pointer and associated permission attributes to be stored in a destination bounded pointer storage element. Furthermore, the processing circuitry marks the source bounded pointer storage element as storing an invalid bounded pointer dependent on whether the copy permission attribute of the source bounded pointer indicates that the source bounded pointer is to be prevented from being subjected to the copy operation. This provides an effective mechanism for inhibiting the subversion of control flow integrity when executing software on the apparatus.