For X with Binomial (n, p) distribution, Section 1 gives a one-page table of .95 and .99 confidence intervals for p, for n = 1, 2, …, 30. This interval is equivariant under X → n − X and p → 1 − p, has approximately equal probability tails, is approximately unbiased, has Crow's property of minimizing the sum of the n + 1 possible lengths, and each of its ends is increasing in X and decreasing in n with about as regular steps as possible. Sections 2 and 3 consider the usual approximate confidence intervals. Calculations and asymptotic results show the need for the continuity correction in these even when n is large. Because of the nonuniformity of the Binomial → Normal convergence as p → 0, these intervals fail to have their stated asymptotic confidence coefficients; simple corrections are given for this. In the approximate interval (X/n) ± {(c/√n)√[(X/n)(1 − X/n)] + 1/(2n)} it is shown that the factor (c/√n) should be replaced by c/√ (n − c2 − 2c/√n − 1/n).