Small to medium enterprises (SMEs) make a key contribution to the economy in terms of employment, innovation and growth. Project management can play a significant role in facilitating this contribution, but SMEs require less bureaucratic forms of project management than those used by larger, traditional organizations. We are undertaking this research to identify the nature of project management required by SMEs, and the results of the qualitative stage of our research are reported in this paper. We interviewed people from companies of the three sizes of SME, micro, small and medium, from a range of industries and from four countries. SMEs use project management both to manage operations, to deliver tailored or bespoke products to customers, and manage innovation and growth. We found similar project management approaches used for both purposes. The main differences occurred by size of company and country. Both Ireland and Sweden looked for more laissez-faire management styles, while people in Austria and Romania were willing to accept more autocratic styles. People in Sweden wanted more structure than people in Ireland. Also laissez-faire styles of management were more appropriate in micro and small companies, whereas more democratic or autocratic styles were needed in medium-sized companies. All three sizes of company wanted less bureaucratic versions of project management than traditional forms, but medium-sized companies, where people fulfil more specialist roles, need more structure than small and micro companies