An acceptable way to assess the quality of an RNG (PRNG) is to apply a standard battery of statistical randomness tests to a sampled output. Such tests compare some observed properties of the sample to properties of a uniform distribution, with the hope to detect deviations from the expected behavior. Consider a (P)RNG that outputs M-bit values which, due to a failure or an attack, are coerced to a subset of {0, 1}Mof only 2nelements, for some n-n> 2-M, but the standard randomness tests do not necessarily detect this behavior. We show here deterministic M-bit sequences (M = 128) that belong to a subset of size 2n, but pass the DIEHARD Battery of Tests of Randomness [1] and the NIST Statistical Test Suite [2], even with a relatively small value of n = 29. To address the difficulty, we propose a detection method that is feasible even for large values of n (e.g., n = 64). As a practical example, we apply our method to rule out the existence of the speculative stealthy hardware Trojan that is discussed in [3].