The Internet and digital devices are increasingly embedded in our everyday lives. The hidden environmental impacts of this infrastructure are substantial and quietly growing at an increasing rate. Our collective Internet use is following a 'Cornucopian paradigm', which is unsustainable. And yet, while intentionally limiting our online connectivity might be seen negatively as a retrograde step, in this paper, we offer ways in which users might welcome attempts to moderate their Internet use through improving four aspects of our digitally-mediated lives: relationships, digital wellbeing, productivity at work, and online privacy. Given these areas, we discuss how our research agenda may realistically be facilitated and what challenges we may face in moving from the reinforcement of 'business as usual' trends. By investigating and developing user-centred, moderate Internet use, we can 'break' the Cornucopian paradigm.