The problem of determining the doping profile minimizing base transit time TB in a BJT is investigated for the case in which the net active dopant dose Q in the quasi-neutral base is held fixed, but the width W of the base is allowed to vary. It is found that the minimum TB is obtained, for reasonable values of Q, by shrinking the base width until the profile becomes box-shaped with doping equal to the solid solubility. This occurs at so narrow a base width, however, that in any practical device it will always be favourable to grade the base doping profile.