Replay attacks are often the most costly attacks to thwart when dealing with off-chip memory integrity. With a trusted System-on-Chip, the existing countermeasures against replay require a large amount of on-chip memory to provide tamper-proof storage for metadata such as hash values or nonces. Tree-based strategies can be deployed to reduce this unacceptable overhead; for example, the well-known Merkle tree technique decreases this overhead to a single hash value. However, it comes at the cost of performance-killing characteristics for embedded systems - e.g. non-parallelizable hash computations on tree updates. In this paper, we propose an alternative solution: the Tamper-Evident Counter Tree (TEC-Tree). It allows for tamper-evident offchip storage of the nonces involved in a replay countermeasure; TEC-Tree parallelizes the computations involved in both the authentication and tree update processes. Moreover, because our tree relies on block encryption, it provides data confidentiality at no extra cost. TEC-Tree is a deployable solution for memory integrity, with low performance hit and hardware cost.