Low-shot object counters estimate the number of objects in an image using fewor no annotated exemplars. Objects are localized by matching them toprototypes, which are constructed by unsupervised image-wide object appearanceaggregation. Due to potentially diverse object appearances, the existingapproaches often lead to overgeneralization and false positive detections.Furthermore, the best-performing methods train object localization by asurrogate loss, that predicts a unit Gaussian at each object center. This lossis sensitive to annotation error, hyperparameters and does not directlyoptimize the detection task, leading to suboptimal counts. We introduce GeCo, anovel low-shot counter that achieves accurate object detection, segmentation,and count estimation in a unified architecture. GeCo robustly generalizes theprototypes across objects appearances through a novel dense object queryformulation. In addition, a novel counting loss is proposed, that directlyoptimizes the detection task and avoids the issues of the standard surrogateloss. GeCo surpasses the leading few-shot detection-based counters by$\sim$∼25% in the total count MAE, achieves superior detection accuracy andsets a new solid state-of-the-art result across all low-shot counting setups.