Deep convolutional neural networks (CNNs) for image denoising are typically trained on large datasets. These models achieve the current state of the art, but they do not generalize well to data that deviate from the training distribution. Recent work has shown that it is possible to train denoisers on a single noisy image. These models adapt to the features of the test image, but their performance is limited by the small amount of information used to train them. Here we propose "GainTuning'', a methodology by which CNN models pre-trained on large datasets can be adaptively and selectively adjusted for individual test images. To avoid overfitting, GainTuning optimizes a single multiplicative scaling parameter (the “Gain”) of each channel in the convolutional layers of the CNN. We show that GainTuning improves state-of-the-art CNNs on standard image-denoising benchmarks, boosting their denoising performance on nearly every image in a held-out test set. These adaptive improvements are even more substantial for test images differing systematically from the training data, either in noise level or image type. We illustrate the potential of adaptive GainTuning in a scientific application to transmission-electron-microscope images, using a CNN that is pre-trained on synthetic data. In contrast to the existing methodology, GainTuning is able to faithfully reconstruct the structure of catalytic nanoparticles from these data at extremely low signal-to-noise ratios.