This article explores the innovation orientation of small and medium-sized enterprises (SMEs) through a quantitative study of 380 Norwegian exporting SMEs. Although recent research emphasises the influence of resource scarcity on SME innovation orientation, we argue that no clear hypothesis can be made about this relationship; rather, we focus on the role of managers and owners in influencing innovation orientation. We find that resource scarcity is not correlated with the innovation orientation of SMEs, while the growth ambitions of managers and owners strongly and positively influence their focus on both exploratory and exploitative innovation. Contrary to our expectations, we find that managerial perception of competitive intensity only moderately influences innovation orientation, while managerial perception of market growth does not influence innovation orientation. Our findings suggest that achieving ambidexterity is primarily a matter of ambition and entrepreneurial capability, rather than an issue of having the necessary resources or lucrative market conditions to innovate ambidextrously. As we also find that ambidextrous SMEs have the strongest innovation performance, our findings indicate that SMEs both can and should be ambidextrous.