This report provides a discussion about the fundamentals of the frequentist approach to the classical nonlinear least squares head - discharge power-law rating curve model, which is a vital procedure in practical hydrology. It is shown that the multivariate minimization problem of the classical nonlinear least squares rating curve model is equivalent to the maximization of a single argument function. We propose four general criteria which the discharge measurements should meet if a trustable frequentist least squares rating curve estimate should exist. The proposed criteria are applied to a large number of real-life discharge measurements, which suggest that the criteria are particularly useful in practice. We also show that the breakdown of one of the criteria implies an exponential law relationship between the head and the discharge. Numerical maximization of the single argument function and inference are discussed.