A system that implements a data storage service may store data for database tables in multiple replicated partitions on respective storage nodes. In response to a request to restore a given table that was backed up in a remote storage system (e.g., key-value durable storage system), the service may create a new table, and may import a copy of each of the partitions of the given table from the remote storage system into the new table. The request to restore the table may specify a modified value for a configuration parameter for the table or for one of its partitions. The service may apply the new configuration parameter value to the table or its partitions during the restore operation. The new configuration parameter value may indicate an increase or decrease in storage capacity or throughput capacity, and its application may automatically trigger a partition split or move operation.