University-industry relations are an important factor for industrial innovation. However, the results of these relationships for the firms remain largely unmeasured. Moreover, the contribution of different types of interactions to firm innovativeness is known mainly in theoretical terms.  Departing from a secondary data of Brazilian university-industry interaction survey, also known as “BR survey”, this study employs crisp-set qualitative comparative analysis (csQCA) to identify how five types of University-industry interactions - training-oriented, service-oriented, diffusion-oriented, development-oriented, and research-oriented - combine to produce high innovation output. The results show that the most complex interactions - development-oriented and research-oriented - are the only types of interactions that alone lead the firm to high innovativeness. In contrast, less complex interactions alone are not enough to make the firm innovate beyond the “new-to-the-firm” level and need to be complemented by more complex interaction.