Non-Volatile Main Memory (NVMM) systems provide high performance by directly manipulating persistent data in-memory, but require crash consistency support to recover data in a consistent state in case of a power failure or system crash. In this work, we focus on the interplay between the crash consistency mechanisms and memory encryption. Memory encryption is necessary for these systems to protect data against the attackers with physical access to the persistent main memory. As decrypting data at every memory read access can significantly degrade the performance, prior works propose to use a memory encryption technique, counter-mode encryption, that reduces the decryption overhead by performing a memory read access in parallel with the decryption process using a counter associated with each cache line. Therefore, a pair of data and counter value is needed to correctly decrypt data after a system crash. We demonstrate that counter-mode encryption does not readily extend to crash consistent NVMM systems as the system will fail to recover data in a consistent state if the encrypted data and associated counter are not written back to memory atomically, a requirement we refer to as counter-atomicity. We show that nȧively enforcing counter-atomicity for all NVMM writes can serialize memory accesses and results in a significant performance degradation. In order to improve the performance, we make an observation that not all writes to NVMM need to be counter-atomic. The crash consistency mechanisms rely on versioning to keep one consistent copy of data intact while manipulating another version directly in-memory. As the recovery process only relies on the unmodified consistent version, it is not necessary to strictly enforce counter-atomicity for the writes that do not affect data recovery. Based on this insight, we propose selective counter-atomicity that allows reordering of writes to data and associated counters when the writes to persistent memory do not alter the recoverable consistent state. We propose efficient software and hardware support to enforce selective counter-atomicity. Our evaluation demonstrates that in a 1/2/4/8- core system, selective counter-atomicity improves performance by 6/11/22/40% compared to a system that enforces counter-atomicity for all NVMM writes. The performance of our selective counter-atomicity design comes within 5% of an ideal NVMM system that provides crash consistency of encrypted data at no cost.