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Pure Q-switching (self-pulsating) behaviour is shown for the first time in an optically injected two-section quantum-dot laser. Upon CW optical injection, it was possible to switch the operation regime from free-running mode-locking to locked Q-switching. Under this regime, the pulse repetition rate of around 1 GHz was tunable with injection power (by more than 100 MHz) and absorber reverse bias. Moreover, through injection-locking, the Q-switched output was spectrally tunable by around 7 nm, by tuning the master laser. The seamless switch between mode-locking and Q-switching with optical injection as well as the tunability and control afforded by injection-locking could open up a range of applications, such as in multi-modal imaging. On a more fundamental level, this investigation has also generated new insights into the dynamics of quantum-dot lasers and the optical injection process.