Memory-based trackers are video object segmentation methods that form the target model by concatenating recently tracked frames into a memory buffer and localize the target by attending the current image to the buffered frames. While already achieving top performance on many benchmarks, it was the recent release of SAM2 that placed memory-based trackers into focus of the visual object tracking community. Nevertheless, modern trackers still struggle in the presence of distractors. We argue that a more sophisticated memory model is required, and propose a new distractor-aware memory model for SAM2 and an introspection-based update strategy that jointly addresses the segmentation accuracy as well as tracking robustness. The resulting tracker is denoted as DAM4SAM. We also propose a new distractor-distilled DiDi dataset to study the distractor problem better. DAM4SAM outperforms SAM2.1 and related SAM memory extensions on seven benchmarks and sets a solid new state-of-the-art on six of them. The code and the new dataset are available on https://github.com/jovanavidenovic/DAM4SAM.