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To achieve more accurate global time synchronization, this paper argues for decoupling the clock distribution network from the routing tree in a multihop wireless network. We find that both flooding and routing-integrated time synchronization rapidly propagate node-level errors (typically due to temperature fluctuations) across the network. Therefore, we propose that a node chooses synchronization neighbors that offer the greatest frequency stability. We propose two methods to estimate a neighbor's stability. The first approach selects the neighbor whose Frequency Error Variance, or simply FEV, is smallest with respect to the local clock. The second approach selects the neighbor that reports the lowest FEV relative to its synchronization parent. We also propose the node-level time-variance FEV as an additive metric for selecting more stable clock trees than either naïve flooding or routing-integrated time synchronization can provide. We incorporate these techniques into FTSP, a widely-used time synchronization protocol, and show that the mean error in global time significantly improved (by a factor of five) when some nodes are warmed and others are not.