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In many measurement applications, it is required to have notch filters that simultaneously possess a very selective magnitude response (high quality factor Q) and a transient response of short duration. However, increasing the quality factor also increases the duration of the transient process in the filter after the action of the excitation. This paper presents a new concept of digital IIR notch filters, whose quality factor changes with time. Owing to a temporary change in the value of the quality factor, the transient can considerably be reduced. Simulations verifying the effectiveness of the proposed Q-varying IIR notch filter are presented and compared with the performance of the traditional Q-constant filter using ECG signals with unwanted sinusoidal interference as a study case.