We review the methodological challenges in the state-of-the-art capabilities for real-time inference of paths that packets travel across the Internet, at the granularity of network service providers, i.e., autonomous system, or ASes. AS path inferences based on control-plane (BGP) data lead to inaccuracies, so researchers have attempted to use traceroute-based inferences to mitigate these inaccuracies, although without a formal framework for doing so. In this work, we improve the state-of-the-art technology for inferring AS paths traversed by traceroute probes in three ways: (i) we introduce a framework to systematically evaluate when different approaches lead to wrong inferences; (ii) we present a methodology that by combining previous and novel inference heuristics yields better accuracy; (iii) we implement in a software tool this methodology and two other methodologies for comparative evaluation. We describe the process we used to construct AS-level paths, the set of heuristics we use to evaluate them, and the tool in which we implemented these heuristics. A more comprehensive evaluation and refinement of these heuristics is future work; we report on the current state of one of the most daunting unresolved measurement challenges on the Internet.