Using eye-tracking, we examined whether overspecification hinders or facilitates referent selection and the extent to which this depends on the properties of the attribute mentioned in the referring expressions and the underpinning processing mode. Following spoken instructions, participants selected the referent in a visual display while their eye movements were monitored. The referring expressions were presented either simultaneously with the displays, so the attributes could be incrementally processed "in sequence," or before the display presentation, so the attributes could be processed "in parallel" from the outset of search. Experiment 1 showed that when the attributes were processed incrementally, how quickly an earlier-mentioned attribute discriminated determined whether a late-mentioned, overspecified attribute contributed to discrimination: When color was mentioned first and was fully discriminating, the referent was selected fast regardless of the second-mentioned pattern, whereas when pattern was mentioned first and fully discriminating, the second-mentioned color facilitated discrimination. Experiment 2 found that under incremental processing, color mention after a fully discriminating pattern increased fixations but delayed referent selection relative to a pattern-only description; under parallel processing, however, color mention immediately eliminated alternatives and sped up referent selection. Experiment 3 showed that pattern mention after a fully discriminating color delayed referent selection and tended to reduce fixations relative to a color-only description in both processing modes. Hence, additional attributes can speed up referent selection but only when they can discriminate much faster than alternative attributes mentioned in a more concise description "and," critically, when they can be used "early" for referent search.