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We develop a job-market signalling model where signals convey two pieces of information. This model is employed to study countersignalling (signals nonmonotonic in ability) and the GED exam. A result of the model is that countersignalling is more likely to occur in jobs that require a combination of skills that differs from the combination used in the schooling process. The model also produces testable implications consistent with evidence on the GED: (i) it signals both high cognitive and low noncognitive skills and (ii) it does not affect wages.