Acoustic echo cancellation (AEC) algorithms have a long-term steady role in signal processing, with approaches improving the performance of applications such as automotive hands-free systems, smart home and loudspeaker devices, or web conference systems. Just recently, very first deep neural network (DNN)-based approaches were proposed with a DNN for joint AEC and residual echo suppression (RES)/noise reduction, showing significant improvements in terms of echo suppression performance. Noise reduction algorithms, on the other hand, have enjoyed already a lot of attention with regard to DNN approaches, with the fully convolutional recurrent network (FCRN) architecture being among state of the art topologies. The recently published impressive echo cancellation performance of joint AEC/RES DNNs, however, so far came along with an undeniable impairment of speech quality. In this work we will heal this issue and significantly improve the near-end speech component quality over existing approaches. Also, we propose for the first time-to the best of our knowledge-a pure DNN AEC in the form of an echo estimator, that is based on a competitive FCRN structure and delivers a quality useful for practical applications.