A method of processing exceptions in an exception-driven computing-based system that operates in either initialisation mode or exception-driven mode. The method includes, upon detecting an exception has occurred, causing the processor to execute exception handling instructions. When the system is operating in initialisation mode the exception handling instructions invoke a first exception handler that causes a main register set to be saved before processing the exception and restored after processing the exception, and when the system is operating in exception-driven mode the exception handling instructions invoke a second exception handler that does not cause the main register set to be saved and restored. In some examples, the exception handling instructions are initially configured to invoke the first exception handler and are dynamically updated when the system switches from initialisation mode to exception-driven mode to invoke the second exception handler.