Despite the emerging experimental techniques for perturbing multiple genes and measuring their quantitative phenotypic effects, genetic interactions have remained extremely difficult to predict on a large scale. Using a recent high-resolution screen of genetic interactions in yeast as a case study, we investigated whether the extraction of pertinent information encoded in the quantitative phenotypic measurements could be improved by computational means. By taking advantage of the observation that most gene pairs in the genetic interaction screens have no significant interactions with each other, we developed a sequential approximation procedure which ranks the mutation pairs in order of evidence for a genetic interaction. The sequential approximations can efficiently remove background variation in the double-mutation screens and give increasingly accurate estimates of the single-mutant fitness measurements. Interestingly, these estimates not only provide predictions for genetic interactions which are consistent with those obtained using the measured fitness, but they can even significantly improve the accuracy with which one can distinguish functionally-related gene pairs from the non-interacting pairs. The computational approach, in general, enables an efficient exploration and classification of genetic interactions in other studies and systems as well.