Last-Level Caches (LLCs) implement the LRU algorithm to exploit temporal locality, but its performance is quite far of Belady's optimal algorithm as the number of ways increases. One of the main reasons because of LRU does not reach good performance in LLCs is that this policy forces a block to descend until the bottom of the stack before eviction. Nevertheless, most of the blocks that leave the MRU position are not referenced again before eviction. This work pursues to select candidate blocks to be victimized before reaching the bottom of the stack. To this end, this work defines the number of MRU-Tours (MRUTs) of a block as the number of times that a block enters in the MRU position during its live time. Based on the fact that most of the blocks exhibit a single MRUT, this work presents the family of MRUT-based algorithms aimed at exploiting this block behavior to improve performance.