Conditional language models still generate unfaithful output that is not supported by their input. These unfaithful generations jeopardize trust in real-world applications such as summarization or human-machine interaction, motivating a need for automatic faithfulness metrics. To implement such metrics, NLI models seem attractive, since they solve a strongly related task that comes with a wealth of prior research and data. But recent research suggests that NLI models require costly additional machinery to perform reliably across datasets, e.g., by running inference on a cartesian product of input and generated sentences, or supporting them with a question-generation/answering step. In this work we show that pure NLI models _can_ outperform more complex metrics when combining task-adaptive data augmentation with robust inference procedures. We propose: (1) Augmenting NLI training data to adapt NL inferences to the specificities of faithfulness prediction in dialogue; (2) Making use of both entailment and contradiction probabilities in NLI, and (3) Using Monte-Carlo dropout during inference. Applied to the TRUE benchmark, which combines faithfulness datasets across diverse domains and tasks, our approach strongly improves a vanilla NLI model and significantly outperforms previous work, while showing favourable computational cost.