Optimal upper bounds for non-negative parameters

Using the techniques of [arXiv:0911.4271], upper bounds for a given confidence level are modified in an optimal fashion to incorporate the a priori information that the parameter being estimated is non-negative. A paradox with different confidence intervals for the same confidence level is clarified. The "lossy compression" nature of the device of confidence intervals is discussed and a "lossless" option to present results is pointed out.