We present an approach to estimating the reflectance of a surface given its camera response. In this approach we first solve the general form of this problem: we calculate the set of all possible surface reflectances, called the metamer set, and then choose a member from this set. Three possibilities in choosing a single reflectance are described here. First, we assume that all reflectances are equally likely and minimize worst-case error. Second, we adopt the assumption that reflectances follow a normal probability distribution and maximize this probability. Finally, we assume that reflectances are smooth and maximize this property. The results of our experiments show that there is significant benefit from the proposed approach in terms of the accuracy of the estimation compared with that of standard estimation methods. Moreover, the present approach introduces a notion of robustness of estimates in the form of error bars.