Compression is widely used in storage systems to reduce the amount of data that is written to physical storage devices, in order to improve both bandwidth and price per GB. In SSDs, which use NAND flash devices, compression also helps to improve endurance, which is limited to a fixed number of raw bytes written to the media, and to reduce garbage-collection overheads. Compression is typically implemented in one of three layers: the application, the file system or the firmware of the storage device. Our main findings are that compression embedded within the SSD outperforms the built-in host-side compression engines of a well-known database and file systems. Therefore we focus on intra-SSD compression schemes. We investigate the effects of compression granularity and the arrangement of compressed data in NAND flash pages on data reduction and the lifetime of the SSD. We compare several schemes in this design space, some taken from the literature and some new.