A paper written with Zack Gehan and Robert Kenny, forthcoming in Telecommunications Policy. Worldwide there is an ongoing policy and regulatory push to make very high speed broadband available as widely as possible. Underlying the policy interventions to support higher speeds is an implicit assumption that higher speeds will enable different (and socially valuable) use. In this paper we empirically test whether higher speed lines are associated with greater household data usage in the UK. We find that after allowing for demographic factors, higher speed in fact has a very limited relationship to traffic. This suggests that mid-speed broadband is not in fact a constraint on household usage (as measured by traffic), and thus the benefits of policy interventions to support higher speeds remain somewhat speculative.