Securing off-chip main memory is essential for protection from adversaries with physical access to systems. However, current secure-memory designs incur considerable performance overheads-A major cause being the multiple memory accesses required for traversing an integrity-Tree, that provides protection against man-in-The-middle attacks or replay attacks. In this paper, we provide a scalable solution to this problem by proposing a compact integrity tree design that requires fewer memory accesses for its traversal. We enable this by proposing new storage-efficient representations for the counters used for encryption and integrity-Tree in secure memories. Our Morphable Counters are more cacheable on-chip, as they provide more counters per cacheline than existing split counters. Additionally, they incur lower overheads due to counter-overflows, by dynamically switching between counter representations based on usage pattern. We show that using Morphable Counters enables a 128-Ary integrity-Tree, that can improve performance by 6.3% on average (up to 28.3%) and reduce system energy-delay product by 8.8% on average, compared to an aggressive baseline using split counters with a 64-Ary integrity-Tree. These benefits come without any additional storage or reduction in security and are derived from our compact counter representation, that reduces the integrity-Tree size for a 16GB memory from 4MB in the baseline to 1MB. Compared to recently proposed VAULT, our design provides a speedup of 13.5% on average (up to 47.4%).