The distribution of spatial attention has mostly been studied for visual events presented within a two-dimensional space. In this study, we examined the distribution of spatial attention in a three-dimensional space (i.e., across the z-axis). Much previous research suggests that attention is universally biased toward stimuli appearing in near space compared to far space. However, the results of some studies suggest this ‘near advantage’ is task-specific, with some tasks instead producing an attention bias toward stimuli in far space. The current study investigated whether two tasks that differ in attentional priorities (i.e., target localization vs target discrimination) differentially bias attention across near and far depth. Across three experiments, we compared target localization and target discrimination tasks when a single target appeared as the stimulus (Experiment 1) and then, for a cue-target task, compared target localization (Experiment 2A) and target discrimination tasks (Experiment 2B). Our results support the proposal that the near advantage is task-specific. For target localization, reaction times (RTs) were shorter for near-targets than for far-targets, however, for target discrimination, RTs were shorter for far-targets than for near-targets. This result was revealed in both uncued and cue-target paradigms. The cue-target paradigm also showed that relative to same-depth conditions, the cueing effect pointed to greater facilitation when orienting attention from far-to-near space for target localization but from near-to-far space for target discrimination. These findings argue against a universal near advantage. Overall, the results were consistent with the notion that different task demands can differentially bias the distribution of attention across near and far depth, a proposal that has implications for the potential involvement of the dorsal and ventral visual processing streams.