Suppose thaty1, …,ykare normal random variables with ordered meansu1≤u2≤ … ≤uk. A confidence bound is found for eachuithat takes advantage of the ordering. The upper and lower bounds are the maximum and minimum values ofxsuch that the hypotheses thatx<uiandui<xare accepted by their respective likelihood ratio tests. These bounds are often more precise than the usual bounds and can be used to determine the safety of a toxin and to bound the virtual safe dose in a low-dose extrapolation. Simultaneous intervals foru1, …,ukare also derived.