With the rapid diffusion of mobile and fixed access platforms, access to broadband services has become widely available in high and medium-income countries. While overcoming gaps in broadband access remains an important and pressing policy issue, the realization of the benefits of advanced information and communication services is increasingly dependent on the quality of the available connectivity. In spite of this increasing importance of quality attributes, such as download and upload speeds, most theoretical and empirical studies of broadband availability have thus far focused on adoption. Only a handful of recent papers have sought to address the factors influencing broadband infrastructure quality. This paper examines the factors that influence the quality of fixed and mobile broadband access. Drawing on institutional economics, the study provides an integrated conceptual framework that allows analyzing the interaction of supply, demand, policy, and contextual factors. This approach allows differentiated insights into the effects of policy choices and their interactions with other factors. Policy instruments that are examined in detail include forms of unbundling and open access, the creation of competitive conditions, and the importance of public-private partnerships. For wireless broadband, we also control for aspects of spectrum policy and management. As is known from policy research, it is often a specific combination of policy choices that affects outcomes rather than any single measure. Prior empirical research suggests that the implementation of a consistent combination of policy choices matters greatly. To address this unique interaction of policy arrangements with outcomes, we pursue a dual approach using empirical methods that allow complementary insights. The application of panel methods allows the examination of sufficient conditions and of effect sizes of drivers of broadband quality. A second method, Qualitative Comparative Analysis (QCA), pioneered by sociologists and political scientists, allows the systematic exploration of interdependencies among these drivers. This quantitative method is better suited than traditional econometric models to explore the interactions between policy choices and the quality of broadband access. QCA allows a systematic examination of the necessary and/or sufficient conditions that influence broadband quality. Because the method is based in principles of set theory, it allows a flexible analysis of not only single policy instruments but also of their interaction with other policy and external conditions. We explore the drivers of both fixed and mobile broadband quality and potential interdependencies between the developments of them. Using Ookla and Akamai data of download speeds that are actually realized over the network infrastructure for a cross-national sample of OECD and medium-income countries, we focus on the role of public policy decisions as a determinant of quality and quality upgrades of access networks. We find that the most important factor with a positive effect on quality and quality improvements is competition. We also find evidence that regulatory interventions such as unbundling or open access provision do have a positive contribution in markets with limited competition. However, the findings also provide evidence that the best policy approach is dependent on the specific context of a country so that no single best practice model emerges from the observations. This paper builds on and significantly expands earlier work, some of which was presented at conferences before (but has not yet been published). A first model of the determinants of fixed broadband quality was presented at the European Regional Conference of the International Telecommunications Society in Florence (October 2013) and a preliminary discussion of QCA with a more limited sample, also focusing on fixed broadband, will be presented at the CPR LATAM conference in Bogota (May 2014). Compared to these earlier versions, the present paper expands the number of countries and adds mobile broadband as well as the interdependencies between fixed and mobile to the analysis.The paper contains methodological, theoretical, and practical contributions. Theoretically, it provides a more comprehensive analysis of the factors that shape broadband speeds. Methodologically, it applies a dual empirical approach to communications policy issues. Because that approach allows exploring the levers available to policy-makers more fully than econometric analyses alone, the paper also contains directly applicable practical lessons for policy-makers.