Today's search engines process billions of online user queries a day over huge collections of data. In order to scale, they distribute query processing among many nodes, where each node holds and searches over a subset of the index called shard. Responses from some nodes occasionally fail to arrive within a reasonable time-interval due to various reasons, such as high server load and network congestion. Search engines typically need to respond in a timely manner, and therefore skip such tail latency responses, which causes degradation in search quality. In this paper, we tackle response misses due to high tail latencies with the goal of maximizing search quality. Search providers today use redundancy in the form of Replication for mitigating response misses, by constructing multiple copies of each shard and searching all replicas. This approach is not ideal, as it wastes resources on searching duplicate data. We propose two strategies to reduce this waste. First, we propose rSmartRed, an optimal shard selection scheme for replicated indexes. Second, when feasible, we propose to replace Replication with Repartition, which constructs independent index instances instead of exact copies. We analytically prove that rSmartRed's selection is optimal for Replication, and that Repartition achieves better search quality compared to Replication. We confirm our results with an empirical study using two real-world datasets, showing that rSmartRed improves recall compared to currently used approaches. We additionally show that Repartition improves over Replication in typical scenarios.