Multiple studies have demonstrated that resolution in working memory (WM) declines as the number of stored items increases. Discrete-resource models predict that this decline should reach a stable plateau at relatively small set sizes because item limits prevent additional information from being encoded into WM at larger set sizes. By contrast, flexible-resource models predict that the monotonic declines in precision will continue indefinitely as set size increases and resources are distributed without any fixed item limit. In the present work, we found that WM resolution exhibited monotonic declines until set size reached three items, after which resolution achieved a clear asymptote. Moreover, analyses of individual differences showed a strong correlation between each observer's item limit and the set size at which WM resolution achieved asymptote. These behavioral observations were corroborated by measurements of contralateral delay activity (CDA), an event-related potential waveform that tracks the number of items maintained during the delay period. CDA activity rose monotonically and achieved asymptote at a set size that predicted individual WM capacity. Moreover, this neural measure of on-line storage also predicted the set size at which mnemonic resolution reached a stable plateau for each observer. Thus, independent behavioral and neural measures of WM capacity support a clear prediction of discrete-resource models. Precision in visual WM reaches asymptote when individual item limits are exceeded.