We show that, for an Euclidean minimal k-insertion tree (EMITk), if the weight w of an edge e is its Euclidean length to the power of α, the sum on all edges of EMITk of their weights w(e) is O(n * k−α/d) in the worst case, where d is the dimension, for d ≥ 2 and 0 < α < d. We also analyze the expected size of EMITk and some stars, when points are evenly distributed inside the unit ball, for any α > 0.