This paper concerns the following problem. Given vertices \(v_ 1,...,v_ n\) with weights \(w_ 1,...,w_ n\), construct a t-ary tree with leaves \(v_ 1,...,v_ n\) in left to right order, such that if \(l_ i\) denotes the length of the path from \(v_ i\) to the root for each i, the maximum of \(w_ i+l_ i\) is minimized. A linear algorithm is presented for the case where all the weights are integers, and this is used to obtain an O(n log n) algorithm for the case of general weights. Moreover it is shown that the minimax value obtained is bounded above by \(2+\log_ t(\sum t^{(w_ i)})\). This result has applications in the study of the effect of fan-out constraints in logical circuits.