Neural machine translation (NMT) is sensitive to domain shift. In this paper, we address this problem in an active learning setting where we can spend a given budget on translating in-domain data, and gradually fine-tune a pre-trained out-of-domain NMT model on the newly translated data. Existing active learning methods for NMT usually select sentences based on uncertainty scores, but these methods require costly translation of full sentences even when only one or two key phrases within the sentence are informative. To address this limitation, we re-examine previous work from the phrase-based machine translation (PBMT) era that selected not full sentences, but rather individual phrases. However, while incorporating these phrases into PBMT systems was relatively simple, it is less trivial for NMT systems, which need to be trained on full sequences to capture larger structural properties of sentences unique to the new domain. To overcome these hurdles, we propose to select both full sentences and individual phrases from unlabelled data in the new domain for routing to human translators. In a German-English translation task, our active learning approach achieves consistent improvements over uncertainty-based sentence selection methods, improving up to 1.2 BLEU score over strong active learning baselines.