Existing temporal relation (TempRel) annotation schemes often have low inter-annotator agreements (IAA) even between experts, suggesting that the current annotation task needs a better definition. This paper proposes a new multi-axis modeling to better capture the temporal structure of events. In addition, we identify that event end-points are a major source of confusion in annotation, so we also propose to annotate TempRels based on start-points only. A pilot expert annotation effort using the proposed scheme shows significant improvement in IAA from the conventional 60's to 80's (Cohen's Kappa). This better-defined annotation scheme further enables the use of crowdsourcing to alleviate the labor intensity for each annotator. We hope that this work can foster more interesting studies towards event understanding.