Recent advances in image-based saliency prediction are approaching gold standard performance levels on existing benchmarks. Despite this success, we show that predicting fixations across multiple saliency datasets remains challenging due to dataset bias. We find a significant performance drop (around 40%) when models trained on one dataset are applied to another. Surprisingly, increasing dataset diversity does not resolve this inter-dataset gap, with close to 60% attributed to dataset-specific biases. To address this remaining generalization gap, we propose a novel architecture extending a mostly dataset-agnostic encoder-decoder structure with fewer than 20 dataset-specific parameters that govern interpretable mechanisms such as multi-scale structure, center bias, and fixation spread. Adapting only these parameters to new data accounts for more than 75% of the generalization gap, with a large fraction of the improvement achieved with as few as 50 samples. Our model sets a new state-of-the-art on all three datasets of the MIT/Tuebingen Saliency Benchmark (MIT300, CAT2000, and COCO-Freeview), even when purely generalizing from unrelated datasets, but with a substantial boost when adapting to the respective training datasets. The model also provides valuable insights into spatial saliency properties, revealing complex multi-scale effects that combine both absolute and relative sizes.