Enhanced Target Collision Resistance (eTCR) property for a hash function was put forth by Halevi and Krawczyk in Crypto 2006, in conjunction with the randomized hashing mode that is used to realize such a hash function family. eTCR is a strengthened variant of the well-known TCR (or UOWHF) property for a hash function family (i.e. a dedicated-key hash function). The contributions of this paper are twofold. First, we compare the new eTCR property with the well-known collision resistance (CR) property, where both properties are considered for a dedicated-key hash function. We show there is a separation between the two notions, that is in general, eTCR property cannot be claimed to be weaker (or stronger) than CR property for any arbitrary dedicated-key hash function. Second, we consider the problem of eTCR property preserving domain extension. We study several domain extension methods for this purpose, including (Plain, Strengthened, and Prefix-free) Merkle-Damg?ard, Randomized Hashing (...