The paper presents a unified approach to classical statistical analysis of small signals, addressing the issue of upper confidence limits for null results and two-sided confidence intervals for non-null results. The authors propose a new method that avoids unphysical confidence intervals and reduces conservatism in the Gaussian case, while maintaining correct frequentist coverage in the Poisson case. They apply this method to two specific problems: Poisson processes with background and Gaussian errors with a bounded physical region. The method is then generalized to analyze experiments searching for neutrino oscillations, demonstrating its correctness and power compared to other classical techniques. The paper also discusses the decoupling of the confidence level used for goodness-of-fit testing from the confidence level used for interval construction, which is a significant advantage of their approach. Finally, it addresses the issue of fewer events than expected background, suggesting that experiments should report both the upper limit and the "sensitivity" to provide more informative results.The paper presents a unified approach to classical statistical analysis of small signals, addressing the issue of upper confidence limits for null results and two-sided confidence intervals for non-null results. The authors propose a new method that avoids unphysical confidence intervals and reduces conservatism in the Gaussian case, while maintaining correct frequentist coverage in the Poisson case. They apply this method to two specific problems: Poisson processes with background and Gaussian errors with a bounded physical region. The method is then generalized to analyze experiments searching for neutrino oscillations, demonstrating its correctness and power compared to other classical techniques. The paper also discusses the decoupling of the confidence level used for goodness-of-fit testing from the confidence level used for interval construction, which is a significant advantage of their approach. Finally, it addresses the issue of fewer events than expected background, suggesting that experiments should report both the upper limit and the "sensitivity" to provide more informative results.