Template-based discriminative trackers are currently the dominant tracking paradigm due to their robustness, but are restricted to bounding box tracking and a limited range of transformation models, which reduces their localization accuracy. We propose a discriminative single-shot segmentation tracker - D3S 2, which narrows the gap between visual object tracking and video object segmentation. A single-shot network applies two target models with complementary geometric properties, one invariant to a broad range of transformations, including non-rigid deformations, the other assuming a rigid object to simultaneously achieve robust online target segmentation. The overall tracking reliability is further increased by decoupling the object and feature scale estimation. Without per-dataset finetuning, and trained only for segmentation as the primary output, D3S 2 outperforms all published trackers on the recent short-term tracking benchmark VOT2020 and performs very close to the state-of-the-art trackers on the GOT-10k, TrackingNet, OTB100 and LaSoT. D3S 2 outperforms the leading segmentation tracker SiamMask on video object segmentation benchmarks and performs on par with top video object segmentation algorithms.