The initial dose setting at the start of the Chronocort® treatment will be based on hydrocortisone dose equivalent of baseline therapy in accordance with standard clinical practice. Further dose refinement/titration will be conducted in both treatment groups as necessary after 4 weeks and 12 weeks using a standardised titration algorithm after the subject has been re-admitted for further 24-hour endocrine profiles. Safety endpoints will also be measured at the 07:00 morning sample of each 24-hour profile assessment day. The decision to change doses in both treatment groups will be made by a central independent blinded physician, with the actual change in dose then being made by the local investigator looking after the subject. At 6 months, all the baseline tests will be repeated (including the 24-hour profile). All subjects may then continue on Chronocort®, whatever their randomised treatment, as part of an open-label extension study (to be conducted under a separate protocol). Stress doses of hydrocortisone will be given throughout the study for intercurrent illnesses as medically indicated according to "sick day rules".