Differentially Private (DP) learning has seen limited success for building large deep learning models of text, and attempts at straightforwardly applying Differentially Private Stochastic Gradient Descent (DP-SGD) to NLP tasks have resulted in large performance drops and high computational overhead. We show that this performance drop can be mitigated with (1) the use of large pretrained models; (2) hyperparameters that suit DP optimization; and (3) fine-tuning objectives aligned with the pretraining procedure. With these factors set right, we obtain private NLP models that outperform state-of-the-art private training approaches and strong non-private baselines – by directly fine-tuning pretrained models with DP optimization on moderately-sized corpora. To address the computational challenge of running DP-SGD with large Transformers, we propose a memory saving technique that allows clipping in DP-SGD to run without instantiating per-example gradients for any layer in the model. The technique enables privately training Transformers with almost the same memory cost as non-private training at a modest run-time overhead. Contrary to conventional wisdom that DP optimization fails at learning high-dimensional models (due to noise that scales with dimension) empirical results reveal that private learning with pretrained models tends to not suffer from dimension-dependent performance degradation.