If the crooks for the first, second, and third valves of a brass instrument are made of the proper lengths to produce respectively a tempered whole tone, a tempered half tone, and a tempered tone and a half, then the notes produced by the simultaneous use of any two or more valves are sharper than the corresponding tempered intervals. The problem of tempering the scale of a valve instrument thus becomes a matter of making each valve crook too long for tempered intervals when the valves are used singly, so that the sharpness of notes produced by the combined use of valves shall be reduced as much as possible. The precise lengths of the several valve crooks for minimizing discrepancies of intonation in a valve instrument appear to be unknown both to writers on acoustics and to makers of valve instruments. The paper presents the method of minimizing such discrepancies.