Systems are increasingly required to provide responses to queries, even if not exact, within stringent time deadlines. These systems parallelize computations over many processes and aggregate them hierarchically to get the final response (e.g. search engines and data analytics). Due to large performance variations in clusters, some processes are slower. Therefore, aggregators are faced with the question of how long to wait for outputs from processes before combining and sending them upstream. Longer waits increase the response quality as it would include outputs from more processes. However, it also increases the risk of the aggregator failing to provide its result by the deadline. This leads to all its results being ignored, degrading response quality. Our algorithm, Cedar, proposes a solution to this quandary of deciding wait durations at aggregators. It uses an online algorithm to learn distributions of durations at each level in the hierarchy and collectively optimizes the wait duration. Cedar’s solution is theoretically sound, fully distributed, and generically applicable across systems that use aggregation trees since it is agnostic to the causes of performance variations. Evaluation using production latency distributions from Google, Microsoft and Facebook using deployment and simulation shows that Cedar improves average response quality by over 100%.