This paper presents a unified approach to classical statistical analysis of small signals, addressing the problem of constructing confidence intervals for both upper limits and two-sided intervals. The method avoids unphysical confidence intervals and eliminates conservatism in the Gaussian case while reducing it in the Poisson case. It is applied to problems involving Poisson processes with background and Gaussian errors with a bounded physical region, and generalized for neutrino oscillation searches. The method uses a novel ordering principle based on likelihood ratios, which ensures that confidence intervals are never unphysical or empty. This approach satisfies the classical criterion of frequentist coverage and is more powerful than other classical techniques used in neutrino oscillation experiments. The method also decouples the calculation of confidence intervals from the goodness-of-fit test, allowing for independent determination of confidence levels. The paper compares the proposed method with alternative classical methods, showing that it provides correct coverage and is more powerful. The method is also applied to the problem of experiments observing fewer events than expected background, where it provides a lower upper limit than experiments observing the expected number of events. The paper concludes that the proposed method is a robust and effective approach to classical statistical analysis of small signals.This paper presents a unified approach to classical statistical analysis of small signals, addressing the problem of constructing confidence intervals for both upper limits and two-sided intervals. The method avoids unphysical confidence intervals and eliminates conservatism in the Gaussian case while reducing it in the Poisson case. It is applied to problems involving Poisson processes with background and Gaussian errors with a bounded physical region, and generalized for neutrino oscillation searches. The method uses a novel ordering principle based on likelihood ratios, which ensures that confidence intervals are never unphysical or empty. This approach satisfies the classical criterion of frequentist coverage and is more powerful than other classical techniques used in neutrino oscillation experiments. The method also decouples the calculation of confidence intervals from the goodness-of-fit test, allowing for independent determination of confidence levels. The paper compares the proposed method with alternative classical methods, showing that it provides correct coverage and is more powerful. The method is also applied to the problem of experiments observing fewer events than expected background, where it provides a lower upper limit than experiments observing the expected number of events. The paper concludes that the proposed method is a robust and effective approach to classical statistical analysis of small signals.