We study the well-quasi-order (wqo) consisting of the set of finite trees with leaf labels coming from an arbitrary wqo Q, ordered by tree homomorphisms which respect the order on the labels. This is a variant of the usual Kruskal tree ordering without infima preservation. We calculate the precise maximal order types of this class of wqos as a function of the maximal order type of the labels Q. In the process, we sharpen some recent results of Friedman and Weiermann [7]. Furthermore, we show a correspondence with indecomposable transfinite sequences with finite range, over elements of the wqo Q, of length less than $\omega ^\omega $. Nash-Williams proved that arbitrary transfinite sequences with finite range are also well-quasi-ordered [17], but there are no known methods to extract bounds on the maximal order type from the proof. More concrete proofs for sequences of length less than $\alpha $ for some $\alpha < \omega ^\omega $ were given by Erdös and Rado [5]. Using the correspondence, we obtain precise bounds for the entire collection of transfinite sequences with finite range of length less than $\omega ^\omega $.