With the exponential growth in size of geometric data, it is becoming increasingly important to make effective use of multilevel caches, limited disk storage, and bandwidth. As a result, recent work in the visualization community has focused either on designing sequential access compression schemes or on producing cache-coherent layouts of (uncompressed) meshes for random access. Unfortunately combining these two strategies is challenging as they fundamentally assume conflicting modes of data access. In this paper, we propose a novel order-preserving compression method that supports transparent random access to compressed triangle meshes. Our decompression method selectively fetches from disk, decodes, and caches in memory requested parts of a mesh. We also provide a general mesh access API for seamless mesh traversal and incidence queries. While the method imposes no particular mesh layout, it is especially suitable for cache-oblivious layouts, which minimize the number of decompressi...