Clipping is a common nonlinear distortion that occurs whenever input or output of an audio system exceeds the supported range. This phenomenon undermines not only the perception of speech quality but also downstream processes utilizing the disrupted signal. Therefore, a real-time-capable, robust, and low-response-time method for speech declipping (SD) is desired. In this work, we introduce DDD (Demucs-Discriminator-Declipper), a real-time-capable speech-declipping deep neural network (DNN) that requires less response time by design. We first observe that a previously untested real-time-capable DNN model, Demucs, exhibits a reasonable declipping performance. Then we utilize adversarial learning objectives to increase the perceptual quality of output speech without additional inference overhead. Subjective evaluation shows that DDD outperforms the baselines by a wide margin in terms of speech quality. We perform detailed waveform and spectral analyses to gain an insight into the output behavior of DDD in comparison to the baselines. Finally, our streaming simulations also show that DDD is capable of sub-decisecond mean response times, outperforming the state-of-the-art DNN approach by a factor of six.