Retrieval-enhanced language models (LMs), which condition their predictions on text retrieved from large external datastores, have recently shown significant perplexity improvements compared to standard LMs. One such approach, the kNN-LM, interpolates any existing LM’s predictions with the output of a k-nearest neighbors model and requires no additional training. In this paper, we explore the importance of lexical and semantic matching in the context of items retrieved by kNN-LM. We find two trends: (1) the presence of large overlapping n-grams between the datastore and evaluation set plays an important factor in strong performance, even when the datastore is derived from the training data; and (2) the kNN-LM is most beneficial when retrieved items have high semantic similarity with the query. Based on our analysis, we define a new formulation of the kNN-LM that uses retrieval quality to assign the interpolation coefficient. We empirically measure the effectiveness of our approach on two English language modeling datasets, Wikitext-103 and PG-19. Our re-formulation of the kNN-LM is beneficial in both cases, and leads to nearly 4% improvement in perplexity on the Wikitext-103 test set.