Embodiments of the invention generally pertain to memory devices and more specifically to reducing the write amplification of memory devices without increasing cache requirements. Embodiments of the present invention may be represented as a modified B+ tree in that said tree comprises a multi-level tree in which all data items are stored in the leaf nodes of the tree. Each non-leaf node in the tree will reference a large number of nodes in the next level down from the tree. Modified B+ trees described herein may be represented as data structures used to map memory device page addresses. The entire modified B+ tree used to map said pages may be stored on the same memory device requiring limited amounts of cache. These embodiments may be utilized by low cost controllers that require good sequential read and write performance without large amounts of cache.