In this paper, we present the joint contribution of Unbabel and IST to the WMT 2021 Metrics Shared Task. With this year's focus on Multidimensional Quality Metric (MQM) as the ground-truth human assessment, our aim was to steer COMET towards higher correlations with MQM. We do so by first pre-training on Direct Assessments and then fine-tuning on z-normalized MQM scores. In our experiments we also show that reference-free COMET models are becoming competitive with reference-based models, even outperforming the best COMET model from 2020 on this year's development data. Additionally, we present COMETinho, a lightweight COMET model that is 19x faster on CPU than the original model, while also achieving state-of-the-art correlations with MQM. Finally, in the QE as a metric'' track, we also participated with a QE model trained using the OpenKiwi framework leveraging MQM scores and word-level annotations.