Let \( u \) be a vertex of a simple connected graph \( G \). Transmission of \( u \), \( Tr_G(u) \) is the sum of all distances between \( u \) and other vertices in \( G \). The Wiener index of \( G \), \( W(G) \), is half of the sum of the transmission of all vertices. The Wiener complexity of \( G \) is the number of different vertex transmissions of \( G \). In this paper, we characterize trees with Wiener complexity at most three, while we discuss the structure of trees with Wiener complexity four and illustrate many cases that arise. The trees of Wiener complexity four have been identified within \( 16 \) categories.