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So-called “tagless” caches have become common as a means to deal with the vast L4 last-level caches (LLCs) enabled by increasing device density, emerging memory technologies, and advanced integration capabilities (e.g., 3-D). Tagless schemes often result in intercache entanglement between tagless cache (L4) and the cache (L3) stewarding its metadata. We explore new cache organization policies that mitigate overheads stemming from the intercache-level replacement entanglement. We incorporate support for explicit tiling shapes that can better match software access patterns to improve the spatial and temporal locality of large block allocations in many essential computational kernels. To address entanglement overheads and pathologies, we propose new replacement policies and energy-friendly mechanisms for tagless LLCs, such as restricted block caching (RBC) and victim tag buffer caching (VBC) to incorporate L4 eviction costs into L3 replacement decisions efficiently. We evaluate our schemes on a range of linear algebra kernels that are software tiled. RBC and VBC demonstrate a reduction in memory traffic of 83/4.4/67% and 69/35.5/76% for 8/32/64 MB L4s, respectively. Besides, RBC and VBC provide speedups of 16/0.3/0.6% and 15.7/1.8/0.8%, respectively, for systems with 8/32/64 MB L4, over a tagless cache with an LRU policy in the L3. We also show that matching the shape of the hardware allocation for each tagless region superblocks to the access order of the software tile improves latency by 13.4% over the baseline tagless cache with reductions in memory traffic of 51% over linear superblocks. [ABSTRACT FROM AUTHOR]