A network storage server includes a main buffer cache to buffer writes requested by clients before committing them to primary persistent storage. The server further uses a secondary cache, implemented as low-cost, solid-state memory, such as flash memory, to store data evicted from the main buffer cache or data read from the primary persistent storage. To prevent bursts of writes to the secondary cache, data is copied from the main buffer cache to the secondary cache speculatively, before there is a need to evict data from the main buffer cache. Data can be copied to the secondary cache as soon as the data is marked as clean in the main buffer cache. Data can be written to secondary cache at a substantially constant rate, which can be at or close to the maximum write rate of the secondary cache.