State-of-the-art stixel methods fuse dense stereo disparity and semantic class information, e.g. from a Convolutional Neural Network (CNN), into a compact representation of driveable space, obstacles and background. However, they do not explicitly differentiate instances within the same semantic class. We investigate several ways to augment single-frame stixels with instance information, which can be extracted by a CNN from the RGB image input. As a result, our novel Instance Stixels method efficiently computes stixels that account for boundaries of individual objects, and represents instances as grouped stixels that express connectivity. Experiments on the Cityscapes dataset demonstrate that including instance information into the stixel computation itself, rather than as a post-processing step, increases the segmentation performance (i.e. Intersection over Union and Average Precision). This holds especially for overlapping objects of the same class. Furthermore, we show the superiority of our approach in terms of segmentation performance and computational efficiency compared to combining the separate outputs of Semantic Stixels and a state-of-the-art pixel-level CNN. We achieve processing throughput of 28 frames per second on average for 8 pixel wide stixels on images from the Cityscapes dataset at 1792x784 pixels. Our Instance Stixels software is made freely available for non-commercial research purposes.