Elevated cortisol in chronic stress and mood disorders causes morbidity including metabolic and cardiovascular diseases. There is therefore interest in developing drugs that lower cortisol by targeting its endocrine pathway, the hypothalamic-pituitary-adrenal (HPA) axis. However, several promising HPA-modulating drugs have failed to reduce long-term cortisol in mood disorders, despite effectiveness in other hypercortisolism conditions such as Cushing's syndrome. The reasons for these failures remain unclear. Here, we use a mathematical model of the HPA axis to demonstrate that the pituitary and adrenal glands compensate for drug effects by adjusting their functional mass, a feedback mechanism absent in Cushing tumors. Our systematic in silico analysis identifies two interventions targeting corticotropin-releasing hormone (CRH) as effective for lowering long-term cortisol. Other targets either fail due to gland mass compensation or harm other aspects of the HPA axis. We propose CRH-neutralizing antibodies and CRH-synthesis inhibitors as potential targets for reducing long-term cortisol in mood disorders and chronic stress. More generally, this study indicates that understanding the slow compensatory mechanisms in endocrine axes can be crucial to prioritize drug targets.