Context: A common assumption in software engineering is that a more structured process delivers higher quality products. However, there are limited empirical studies that support this assumption. Objective: In this paper we analyze 61 projects looking for a relationship between process structuredness and quality of the product. Method: The structuredness is considered under two dimensions: level of maturity (as measured by the CMMI assessment model) and type (e.g. TSP, RUP). The quality of the product is measured in terms of Defect Density (DD) defined as the number of delivered defects divided per size. Results: We found a small and statistically not significant difference of DD between the projects developed under CMMI and those that are not developed under CMMI. Considering the CMMI levels, the pair (CMMI 1, CMMI 3) is characterized by a statistically significant different DD. CMMI 1 exhibiting higher DD than CMMI 3. By comparing different software processes with each other we found that Hybrid process exhibits statistically significant lower DD than Waterfall. Conclusion: Software process in either dimension, level of maturity and type has an impact on the software quality but smaller than one might expect.