High accuracy, synchronized clocks are essential to a growing number of Internet applications. Standard protocols and their associated server infrastructure typically enable client clocks to synchronize to the order of tens of milliseconds. We address one of the key challenges to high precision Internet timekeeping - the intrinsic contribution to clock error of underlying path asymmetry between client and time server, a fundamental barrier to microsecond level accuracy. We first exploit results of a unique measurement study to reliably quantify asymmetry by taking routing changes into account for the first time, and then to infer the impacts on timing. We then describe three approaches to addressing the path asymmetry problem: LBBE, SBBE and K-SBBE, each based on timestamp exchange with multiple servers, with the goal of tightening bounds on asymmetry for each client. We explore their capabilities and limitations through simulation and model-based argument. We show that substantial imp