For most complex traits, DNA-based heritability ('SNP heritability') is roughly half that of twin-based heritability. A previous report from the Twins Early Development Study suggested that this heritability gap is much greater for childhood behaviour problems than for other domains. If true, this finding is important because SNP heritability, not twin heritability, is the ceiling for genome-wide association studies. With twice the sample size as the previous report, we estimated SNP heritabilities (N up to 4653 unrelated individuals) and compared them with twin heritabilities from the same sample (N up to 4724 twin pairs) for diverse domains of childhood behaviour problems as rated by parents, teachers, and children themselves at ages 12 and 16. For 37 behaviour problem measures, the average twin heritability was 0.52, whereas the average SNP heritability was just 0.06. In contrast, results for cognitive and anthropometric traits were more typical (average twin and SNP heritabilities were 0.58 and 0.28, respectively). Future research should continue to investigate the reasons why SNP heritabilities for childhood behaviour problems are so low compared with twin estimates, and find ways to maximise SNP heritability for genome-wide association studies.