Adaptive inference is a simple method for reducing inference costs. The method works by maintaining multiple classifiers of different capacities, and allocating resources to each test instance according to its difficulty. In this work, we compare the two main approaches for adaptive inference, Early-Exit and Multi-Model, when training data is limited. First, we observe that for models with the same architecture and size, individual Multi-Model classifiers outperform their Early-Exit counterparts by an average of 2.3%. We show that this gap is caused by Early-Exit classifiers sharing model parameters during training, resulting in conflicting gradient updates of model weights. We find that despite this gap, Early-Exit still provides a better speed-accuracy trade-off due to the overhead of the Multi-Model approach. To address these issues, we propose SWEET (Separating Weights for Early-Exit Transformers) an Early-Exit fine-tuning method that assigns each classifier its own set of unique model weights, not updated by other classifiers. We compare SWEET’s speed-accuracy curve to standard Early-Exit and Multi-Model baselines and find that it outperforms both methods at fast speeds while maintaining comparable scores to Early-Exit at slow speeds. Moreover, SWEET individual classifiers outperform Early-Exit ones by 1.1% on average. SWEET enjoys the benefits of both methods, paving the way for further reduction of inference costs in NLP.