LSM-based KV stores are designed to offer good write performance, by capturing client writes in memory, and only later flushing them to storage. Writes are later compacted into a tree-like data structure on disk to improve read performance and to reduce storage space use. It has been widely documented that compactions severely hamper throughput. Various optimizations have successfully dealt with this problem. These techniques include, among others, rate-limiting flushes and compactions, selecting among compactions for maximum effect, and limiting compactions to the highest level by so-called fragmented LSMs. In this paper we focus on latencies rather than throughput. We first document the fact that LSM KVs exhibit high tail latencies. The techniques that have been proposed for optimizing throughput do not address this issue, and in fact in some cases exacerbate it. The root cause of these high tail latencies is interference between client writes, flushes and compactions. We then introduce the notion of an I/O scheduler for an LSM-based KV store to reduce this interference. We explore three techniques as part of this I/O scheduler: 1) opportunistically allocating more bandwidth to internal operations during periods of low load, 2) prioritizing flushes and compactions at the lower levels of the tree, and 3) preempting compactions. SILK is a new open-source KV store that incorporates this notion of an I/O scheduler. SILK is derived from RocksDB, but the concepts can be applied to other LSM-based KV stores. We use both a production workload at Nutanix and synthetic benchmarks to demonstrate that SILK achieves up to two orders of magnitude lower 99th percentile latencies than RocksDB and TRIAD, without any significant negative effects on other performance metrics.