With the emergence of pervasive 64 bit computing we observe that it is more cost effective to compute a SHA-512 than it is to compute a SHA-256 over a given size of data. We propose a standard way to use SHA-512 and truncate its output to 256 bits. For 64 bit architectures, this would yield a more efficient 256 bit hashing algorithm, than the current SHA-256. We call this method SHA-512/256. We also provide a method for reducing the size of the SHA-512 constants table that an implementation will need to store.