Traditionally, students with learning disabilities (LD) have been identified using an aptitude–achievement discrepancy or response to intervention approach. As profiles of the cognitive deficits of discrepancy-defined students with LD have already been developed using these approaches, these deficits can in turn be used to identify LD using the discrepancy approach as a benchmark for convergent validity. Australian Grade 3 (N = 172) students were administered cognitive processing tests to ascertain whether scores in these tests could accurately allocate students into discrepancy-defined groups using discriminant function analysis. Results showed that 77% to 82% of students could be correctly allocated into LD, low achievement, and regular achievement groups using only measures of phonological processing, rapid naming, and verbal memory. Furthermore, verbal memory deficits were found, along with phonological processing and rapid naming deficits, in students that would be designated as low achieving by the discrepancy method. Because a significant discrepancy or lack of response to intervention is a result of cognitive deficits rather than the other way around, it is argued that LD should be identified via cognitive deficits.