In many real-life situations, we know the upper bound of the measurement errors, and we also know that the measurement error is the joint result of several independent small effects. In such cases, due to the Central Limit theorem, the corresponding probability distribution is close to Gaussian, so it seems reasonable to apply the standard Gaussian-based statistical techniques to process this data -- in particular, when we need to identify a system. Yes, in doing this, we ignore the information about the bounds, but since the probability of exceeding them is small, we do not expect this to make a big difference on the result. Surprisingly, it turns out that in some practical situations, we get a much more accurate estimates if we, vice versa, take into account the bounds -- and ignore all the information about the probabilities. In this paper, we explain the corresponding algorithms. and we show, on a practical example, that using this algorithm can indeed leave to a drastic improvement in estimation accuracy.