A data processing apparatus comprising: processing circuitry configured to perform data processing operations in response to program code, the processing circuitry comprising exception control circuitry for controlling exception processing; a data store configured to store data, the data store comprising a plurality of regions including a secure region and a less secure region, wherein the secure region is for storing data which is accessible by the processing circuitry when operating in a secure domain and not accessible by the processing circuitry when operating in a less secure domain; and a plurality of registers configured to store data, the registers including a first subset of registers and a second subset of registers, the registers being accessible to said program code executing on the processing circuitry and, in response to an exception, state saving of data from the registers to the data store being required in order to allow later restoring of that data to the registers when the exception has been handled; wherein: in response to an initial exception from background processing performed by the processing circuitry, the exception control circuitry is configured to perform state saving of data from the first subset of registers to the data store before triggering the processing circuitry to perform an exception handling routine corresponding to the exception, wherein the exception handling routine has responsibility for performing state saving of data from the second subset of registers to the data store; and in response to a first exception causing a transition from the secure domain to the less secure domain, where the background processing was performed by the processing circuitry in the secure domain, the exception control circuitry is configured to perform additional state saving of the data from the second subset of registers to the data store before triggering the processing circuitry to perform the exception handling routine in the less secure domain. processing circuitry configured to perform data processing operations in response to program code, the processing circuitry comprising exception control circuitry for controlling exception processing; a data store configured to store data, the data store comprising a plurality of regions including a secure region and a less secure region, wherein the secure region is for storing data which is accessible by the processing circuitry when operating in a secure domain and not accessible by the processing circuitry when operating in a less secure domain; and a plurality of registers configured to store data, the registers including a first subset of registers and a second subset of registers, the registers being accessible to said program code executing on the processing circuitry and, in response to an exception, state saving of data from the registers to the data store being required in order to allow later restoring of that data to the registers when the exception has been handled; wherein: in response to an initial exception from background processing performed by the processing circuitry, the exception control circuitry is configured to perform state saving of data from the first subset of registers to the data store before triggering the processing circuitry to perform an exception handling routine corresponding to the exception, wherein the exception handling routine has responsibility for performing state saving of data from the second subset of registers to the data store; and in response to a first exception causing a transition from the secure domain to the less secure domain, where the background processing was performed by the processing circuitry in the secure domain, the exception control circuitry is configured to perform additional state saving of the data from the second subset of registers to the data store before triggering the processing circuitry to perform the exception handling routine in the less secure domain. in response to an initial exception from background processing performed by the processing circuitry, the exception control circuitry is configured to perform state saving of data from the first subset of registers to the data store before triggering the processing circuitry to perform an exception handling routine corresponding to the exception, wherein the exception handling routine has responsibility for performing state saving of data from the second subset of registers to the data store; and in response to a first exception causing a transition from the secure domain to the less secure domain, where the background processing was performed by the processing circuitry in the secure domain, the exception control circuitry is configured to perform additional state saving of the data from the second subset of registers to the data store before triggering the processing circuitry to perform the exception handling routine in the less secure domain.