The recent publication of the `InterTubes' map of long-haul fiber-optic cables in the contiguous United States invites an exciting question: how much faster would the Internet be if routes were chosen to minimize latency? Previous measurement campaigns suggest the following rule of thumb for estimating Internet latency: multiply line-of-sight distance by 2.1, then divide by the speed of light in fiber. But a simple computation of shortest-path lengths through the conduits in the InterTubes map suggests that the conversion factor for all pairs of the 120 largest population centers in the U.S.\ could be reduced from 2.1 to 1.3, in the median, even using less than half of the links. To determine whether an overlay network could be used to provide shortest paths, and how well it would perform, we used the diverse server deployment of a CDN to measure latency across individual conduits. We were surprised to find, however, that latencies are sometimes much higher than would be predicted by conduit length alone. To understand why, we report findings from our analysis of network latency data from the backbones of two Tier-1 ISPs, two scientific and research networks, and the recently built fiber backbone of a CDN.