We extend earlier analyses of the job creation of start-ups vs. established firms by taking into consideration the educational content of the jobs created and destroyed. We define education-specific measures of job creation and job destruction at the firm level, and we use these to construct a measure of "surplus job creation" defined as jobs created on top of any simultaneous destruction of similar jobs in incumbent firms in the same region and industry. Using Danish employer-employee data from 2002-7, which identify the start-ups and which cover almost the entire private sector, these measures allow us to provide a more nuanced assessment of the role of entrepreneurial firms in the job-creation process than previous studies. Our findings show that while start-ups are responsible for the entire overall net job creation, incumbents account for more than a third of net job creation within high-skilled jobs. Moreover, start-ups "only" create around half of the surplus jobs, and even less of the high-skilled surplus jobs. Finally, our approach allows us to characterize and identify differences across industries, educational groups and regions.