Confidence judgments in 2-alternative decisions have been the subject of a great deal of research in cognitive psychology. Sequential sampling models have been particularly successful at explaining confidence judgments in such decisions and the relationships between confidence, accuracy, and response latencies. Across 5 experiments, we derived predictions from sequential sampling models and applied them to more complex decisions: multiple-alternative decisions, and compound decisions, such as eyewitness identification tasks, in which a target may be present or absent within the array of items that can be selected. We hypothesized that, when a decision-maker chooses an item, confidence in that decision reflects the relative evidence for the chosen item over all unchosen items. We tested this hypothesis by manipulating the similarity between the target (or target-replacement, for trials in which the target was not present in the array) and the weakest lure(s). As target-lure similarity decreased, confidence in correct target identifications increased, while response latencies decreased. When the decision-maker chose none of the items, the similarity between the target-replacement and the lures was unrelated to confidence. We conclude that similar mechanisms underpin confidence judgments in multiple-alternative and positive compound decisions as in simpler, 2-alternative decisions. A goal of future research should be to formally extend sequential sampling models to more complex decisions, such that it will be possible to establish whether diffusion or accumulator models provide a better fit to the data.