We study the utility of the lexical translation model (IBM Model 1) for English text retrieval, in particular, its neural variants that are trained end-to-end. We use the neural Model1 as an aggregator layer applied to context-free or contextualized query/document embeddings. This new approach to design a neural ranking system has benefits for effectiveness, efficiency, and interpretability. Specifically, we show that adding an interpretable neural Model 1 layer on top of BERT-based contextualized embeddings (1) does not decrease accuracy and/or efficiency; and (2) may overcome the limitation on the maximum sequence length of existing BERT models. The context-free neural Model 1 is less effective than a BERT-based ranking model, but it can run efficiently on a CPU (without expensive index-time precomputation or query-time operations on large tensors). Using Model 1 we produced best neural and non-neural runs on the MS MARCO document ranking leaderboard in late 2020.