We present new orbits for sixteen Ap spectroscopic binaries, four of which might in fact be Am stars, and give their orbital elements. Four of them are SB2 systems: HD 5550, HD 22128, HD 56495 and HD 98088. The twelve other stars are: HD 9996, HD 12288, HD 40711, HD 54908, HD 65339, HD 73709, HD 105680, HD 138426, HD 184471, HD 188854, HD 200405 and HD 216533. Rough estimates of the individual masses of the components of HD 65339 (53 Cam) are given, combining our radial velocities with the results of speckle interferometry and with Hipparcos parallaxes. Considering the mass functions of 74 spectroscopic binaries from this work and from the literature, we conclude that the distribution of the mass ratio is the same for cool Ap stars and for normal G dwarfs. Therefore, the only differences between binaries with normal stars and those hosting an Ap star lie in the period distribution: except for the case of HD 200405, all orbital periods are longer than (or equal to) 3 days. A consequence of this peculiar distribution is a deficit of null eccentricities. There is no indication that the secondary has a special nature, like e. g. a white dwarf.