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Coexistence of trees and grasses in savannas should be possible if competition between the woody and the grassy components is less intense than the competition within each component. Although several studies have investigated competition between trees and grasses, little is known about tree-tree interactions. We used a multi-proxy approach to examine the spatial pattern of Acacia mellifera and other savanna woody species in a semi-arid savanna in South Africa. Spatial analysis of the point patterns of young and reproductively mature shrubs detected decreasing aggregation with size/age over all spatial scales. This indicated the prevalence of competition although the overall spatial shrub pattern was aggregated. In contrast to point pattern statistics that detect changes only when competition has led to the death of the inferior competitor, we also applied methods identifying the competitive effect on sizes of individual trees. Competition should lead to a negative spatial autocorrelation in size, which we observed in half of the studied cases. Quantile regressions show that nearest-neighbour distance increased steeply with combined size of the target shrub and its neighbours indicating strong competitive effects. The medians of the distributions of maximum root lengths of A. mellifera, of the scale of regular patterns, and of negative autocorrelations were not significantly different, suggesting that overlapping root systems mediate competitive interactions. A competitor removal experiment did not lead to increased shrub sizes, which may be due to the limited duration of the experiment. From the nearest neighbour and autocorrelation analyses, we conclude that competition had a strong impact on growth rates of savanna woody species. Competition-induced mortality only becomes obvious when analysing the shift towards less aggregated spatial patterns when shrubs become reproductively mature. As the overall clustered spatial pattern masks the perceptible effect of competition, a time component should always be included in spatial pattern-based inference of competition.