Recent pedestrian detection methods generally rely on additional supervision, such as visible bounding-box annotations, to handle heavy occlusions. We propose an approach that leverages pedestrian count and proposal similarity information within a two-stage pedestrian detection framework. Both pedestrian count and proposal similarity are derived from standard full-body annotations commonly used to train pedestrian detectors. We introduce a count-weighted detection loss function that assigns higher weights to the detection errors occurring at highly overlapping pedestrians. The proposed loss function is utilized at both stages of the two-stage detector. We further introduce a count-and-similarity branch within the two-stage detection framework, which predicts pedestrian count as well as proposal similarity. Lastly, we introduce a count and similarity-aware NMS strategy to identify distinct proposals. Our approach requires neither part information nor visible bounding-box annotations. Experiments are performed on the CityPersons and CrowdHuman datasets. Our method sets a new state-of-the-art on both datasets. Further, it achieves an absolute gain of 2.4% over the current state-of-the-art, in terms of log-average miss rate, on the heavily occluded (HO) set of CityPersons test set. Finally, we demonstrate the applicability of our approach for the problem of human instance segmentation. Code and models are available at: https://github.com/Leotju/CaSe.