Quantification of competition on the single-tree level was assesed in a forest reserve in Norway. Three new classes (non-spatially explicit, spatially explicit and hybrid) of tree competition indices based on airborne laser scanning were derived. By comparison to a selection of existing competition indices both spatially and non-spatially explicit, it was concluded by the performance of a growth model fitted using the competition indices as independent variables, that the ability to predict the diameter growth at breast height of individual trees of Norway spruce (Picea abies (L.) Karst.) was better for many of the derived competition indices, than for the existing competition indices. In addition, the Spearman rank correlation for the best derived index calculated on plot level revealed a highly significant correlation (p < 0.001) between diameter growth at breast height and competition ranging from −0.81 to −0.18 on plot basis. For data pooled from 20 plots used in the study the best of the derived indices increased the adjusted R2 of the growth model by 18%, when compared to the adjusted R2 of a growth model excluding competition as an independent variable. The best of the existing indices increased it by 10%. Some of the derived indices only require the spatial location and properties (diameter at breast height, crown width, height to base of crown and total height) of the subject tree, and not of the competing trees. Logic shows that such indices eliminate plot edge bias, which was supported empirically. When airborne laser scanning data is available, these competition indices should be preferred.