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A closed-form non-parametric detector for rare targets in hyperspectral images is developed, extending the so-called Veritas approach, which until now had been explored only for parametric background models. By treating the typically unknown target fill-factor as known and equal to the smallest value that can be detected at a given level of detectability, an admissible NP detector is obtained. Experimental results on a hyperspectral target detection scenario reveals the potential of the proposed approach, and sets the path for developing more complex but still mathematically and computationally tractable non-parametric admissible detectors based on multiple discrete target fill-factors.