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Man-made scenes are often densely packed, containing numerous objects, often identical, positioned in close proximity. We show that precise object detection in such scenes remains a challenging frontier even for state-of-the-art object detectors. We propose a novel, deep-learning based method for precise object detection, designed for such challenging settings. Our contributions include:(1) A layer for estimating the Jaccard index as a detection quality score;(2) a novel EM merging unit, which uses our quality scores to resolve detection overlap ambiguities; finally,(3) an extensive, annotated data set, SKU-110K, representing packed retail environments, released for training and testing under such extreme settings. Detection tests on SKU-110K, and counting tests on the CARPK and PUCPR+, show our method to outperform existing state-of-the-art with substantial margins.