A wearable cardioverter defibrillator (WCD) including a support structure configured to be worn by an ambulatory patient, an energy storage module configured to store an electrical charge, a discharge circuit coupled to the energy storage module, electrodes configured to render an electrocardiogram (ECG) signal of the patient while the patient is wearing the support structure, a user interface configured to output an alarm in response to a noise alarm signal, and a processor. The processor is configured to receive the ECG signal, determine whether noise is present on the ECG signal, determine from the ECG signal whether a shock criterion is met, and cause the user interface to generate the noise alarm signal when the noise is present on the ECG signal and the shock criterion is met and not generate the noise alarm signal when noise is present on the ECG signal and the shock criterion is not met.