The instrumentalist argument from the underdetermination of theories by data runs as follows: (1) every theory has empirically equivalent rivals; (2) the only warrant for believing one theory over another is its possession of a greater measure of empirical virtue; (3) therefore belief in any theory is arbitrary. In this paper, I examine the status of the first premise. Several arguments against the universal availability of empirically equivalent theoretical rivals are criticized, and four algorithms for producing empirically equivalent rivals are (...) defended. I conclude that the case for the first premise of the argument from underdetermination is very strong. The disposition of the argument itself depends on the fate of the second premise. (shrink)