Neural language models predict the next token using a latent representation of the immediate token history. Recently, various methods for augmenting neural language models with an attention mechanism over a differentiable memory have been proposed. For predicting the next token, these models query information from a memory of the recent history which can facilitate learning mid- and long-range dependencies. However, conventional attention mechanisms used in memory-augmented neural language models produce a single output vector per time step. This vector is used both for predicting the next token as well as for the key and value of a differentiable memory of a token history. In this paper, we propose a neural language model with a key-value attention mechanism that outputs separate representations for the key and value of a differentiable memory, as well as for encoding the next-word distribution. This model outperforms existing memory-augmented neural language models on two corpora. Yet, we found that our method mainly utilizes a memory of the five most recent output representations. This led to the unexpected main finding that a much simpler model based only on the concatenation of recent output representations from previous time steps is on par with more sophisticated memory-augmented neural language models.