A data processing device comprises a plurality of system registers and a set of interrupt handling registers for controlling handling of an incoming interrupt. The device also includes processing circuitry configured to execute software of the plurality of execution levels, and interrupt controller circuitry configured to route said incoming interrupts to interrupt handling software that is configured to run at one of said plurality of execution levels, and register access control circuitry configured to dynamically control access to at least some of said interrupt handling registers in dependence upon one of said plurality of execution levels that said incoming interrupt is routed to. The interrupt handling software configured to run at a particular execution level does not have access to interrupt handling registers for handling a different incoming interrupt that is routed to interrupt handling software that is configured to run at a more privileged execution level.