Processing circuitry can operate in a secure domain and a less secure domain. In response to an initial exception from background processing performed by the processing circuitry, state saving of data from a first subset of registers is performed by exception control circuitry before triggering an exception handling routine, while the exception handling routine has responsibility for performing state saving of data from a second subset of registers. In response to a first exception causing a transition from the secure domain from a less secure domain, where the background processing was in the less secure domain, the exception control circuitry performs additional state saving of data from the second set of registers before triggering the exception handling routine. In response to a tail-chained exception causing a transition from the secure domain to the less secure domain, the exception handling routine is triggered without performing an additional state saving.