The best methods for knowledge graph completion use a ‘dual-encoding’ framework, a form of neural model with a bottleneck that facilitates fast approximate search over a vast collection of candidates. These approaches are trained using contrastive learning to differentiate between known positive examples and sampled negative instances. The mechanism for sampling negatives to date has been very simple, driven by pragmatic engineering considerations (e.g., using mismatched instances from the same batch). We propose several novel means of finding more informative negatives, based on searching for candidates with high lexical overlaps, from the dual-encoder model and according to knowledge graph structures. Experimental results on four benchmarks show that our best single model improves consistently over previous methods and obtains new state-of-the-art performance, including the challenging large-scale Wikidata5M dataset. Combing different kinds of strategies through model ensembling results in a further performance boost.