The labour market rewards for a number of required human capital competences are analysed using a sample of young European higher education graduates. Factor analysis is applied to classify competences by jobs into eight orthogonal groups, namely participative, methodological, specialised, organisational, applying rules, physical, generic and socio-emotional competences. Estimates for the total rewards for competences are obtained through conventional wage regression, whereas estimates of the total rewards are derived in terms of job satisfaction through ordered logit regression. Explanatory variables include personal characteristics, job attributes, occupational titles, fields of study, type of higher education institution and country dummies. Results on wage rewards show that jobs with higher requirements of "participative and methodological competences" are best paid; conversely, jobs with higher requirements of "organisational", "applying-rules" and "physical competences" are worse paid. Results on total rewards suggest that jobs with higher requirements of competences increase graduates' satisfaction, the only exception being "applying-rules competences".