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Target speech extraction, which extracts a single target source in a mixture given clues about the target speaker, has attracted increasing attention. We have recently proposed SpeakerBeam, which exploits an adaptation utterance of the target speaker to extract his/her voice characteristics that are then used to guide a neural network towards extracting speech of that speaker. SpeakerBeam presents a practical alternative to speech separation as it enables tracking speech of a target speaker across utterances, and achieves promising speech extraction performance. However, it sometimes fails when speakers have similar voice characteristics, such as in same-gender mixtures, because it is difficult to discriminate the target speaker from the interfering speakers. In this paper, we investigate strategies for improving the speaker discrimination capability of SpeakerBeam. First, we propose a time-domain implementation of SpeakerBeam similar to that proposed for a time-domain audio separation network (TasNet), which has achieved state-of-the-art performance for speech separation. Besides, we investigate (1) the use of spatial features to better discriminate speakers when microphone array recordings are available, (2) adding an auxiliary speaker identification loss for helping to learn more discriminative voice characteristics. We show experimentally that these strategies greatly improve speech extraction performance, especially for same-gender mixtures, and outperform TasNet in terms of target speech extraction.