This is the first study exploring relationships between sluggish cognitive tempo (SCT) and sleep, internalizing, externalizing, somatic, and cognitive problems in elementary school children using subjective and objective sleep measures. From a population-based sample, 665 children (6-12 years of age) were rated by their mothers on the Pediatric Behavior Scale (PBS) and underwent an overnight polysomnography (PSG) in a sleep laboratory to assess physiologic sleep and its stages. The strongest independent predictors of SCT were maternal ratings of cognitive problems, sleeping more than normal, and somatic complaints, which were more powerful predictors than ratings of reduced sleep, disturbed/fragmented sleep, inattention, impulsivity, hyperactivity, depression, anxiety, oppositional defiant disorder, and conduct disorder. PSG scores were not associated with SCT. The strong predictive power of cognitive problems supports the notion that SCT is related to cognitive deficits, although SCT was also associated with diverse noncognitive problems. The finding that sleeping more than normal was the second strongest predictor of SCT suggests that physiological hypoarousal may help explain the connection between SCT and excessive sleep. The third most powerful predictor of SCT was somatic complaints, which is a critical finding because the association between SCT and somatic problems is under-studied. Results strongly support the SCT construct, including its convergent and divergent validity, internal consistency, and consistent factor composition across diagnostic groups and research samples.