Abstract: Low-shot counters estimate the number of objects corresponding to a selected category, based on only few or no exemplars annotated in the image. The current state-of-the-art estimates the total counts as the sum over the object location density map, but do not provide object locations and sizes, which are crucial for many applications. This is addressed by detection-based counters, which, howeverfall behind in the total count accuracy. Furthermore, both approaches tend to overestimate the counts in the presence of other object classes due to many false positives. We propose DAVE, a low-shot counter based on a detect-and-verify paradigm, that avoids the aforementioned issues by first generating a high-recall detection set and then verifying the detections to identify and remove the outliers.This jointly increases the recall and precision, leading to accurate counts. DAVE outperforms the top density-based counters by $\sim$20\% in the total count MAE, it outperforms the most recent detection-based counter by $\sim$20\% in detection quality, and sets a new state-of-the-art in zero-shot as well as text-prompt-based counting.