This paper describes an algorithm for computing best l1, l2 and l∞ approximations to discrete data, by functions of several parameters which depend nonlinearly on just one of these parameters. Such functions (e.g. a1 + a2ecx, a1 + a2 sin cx, (a1 + a2x)/(1 + cx)) often occur in practice, and a numerical study confirms that it is feasible to compute best approximations in any of the above norms when using these functions. Some remarks on the theory of best l1 approximations by these functions are included.