For constructing confidence intervals for a binomial proportion p, Simon (1996, Teaching Statistics) advocates teaching one of two large-sample alternatives to the usual z-intervals p^​±1.96×S.E(p^​) where S.E.(p^​)=p^​×(1−p^​)/n​. His recommendation is based on the comparison of the closeness of the achieved coverage of each system of intervals to their nominal level. This teaching note shows that a different alternative to z-intervals, called q-intervals, are strongly preferred to either method recommended by Simon. First, q-intervals are more easily motivated than even z-intervals because they require only a straightforward application of the Central Limit Theorem (without the need to estimate the variance of p^​ and to justify that this perturbation does not affect the normal limiting distribution). Second, q-intervals do not involve ad-hoc continuity corrections as do the proposals in Simon. Third, q-intervals have substantially superior achieved coverage than either system recommended by Simon