In embodiments, a Wearable Cardioverter Defibrillator (WCD) system includes a support structure for the patient to wear, and components that the support structure maintains on the patient's body. The components include a defibrillator, associated electrodes, and so on. The defibrillator can operate in a WCD mode while the patient wears the support structure. The defibrillator can further operate in a different, AED mode, during which time the patient need not wear a portion of the support structure, or even the entire support structure. Sometimes the AED mode is a type of a fully automatic AED mode. Other times the AED mode is a type of a semi-automated AED mode, where an attendant is present to administer the shock; at such times, the patient may not even need to have electrodes attached. This way the patient is more comfortable for a longer time.