j-lanes tree hashing is a tree mode that splits an input message into j slices, computes j independent digests of each slice, and outputs the hash value of their concatenation. j-pointers tree hashing is a similar tree mode that receives, as input, j pointers to j messages (or slices of a single message), computes their digests and outputs the hash value of their concatenation. Such modes expose parallelization opportunities in a hashing process that is otherwise serial by nature. As a result, they have a performance advantage on modern processor architectures. This paper provides precise specifications for these hashing modes, proposes appropriate IVs, and demonstrates their performance on the latest processors. Our hope is that it would be useful for standardization of these modes.