The circumvention-of-limits hypothesis holds that the more skilled and knowledgeable the task performer, the less it matters for task performance whether that person has limited general cognitive ability. We tested this hypothesis using a knowledge activation approach to manipulate knowledge experimentally. The criterion task, which we designed to capture a fundamental requirement of a broad class of real-world tasks, was a placekeeping task in which participants had to perform a sequence of operations in a specified order, applying 7 different 2-alternative decision rules to a series of randomly generated stimuli. The measures of interest in this task were response time and accuracy, as well as frequency of use of a help function to recall the correct sequence of steps. In the knowledge-activated condition, we gave participants a mnemonic in which the first letters of the decision rules spelled the English word unravel. In the knowledge-not-activated condition, no mnemonic was given, and the use and discovery of mnemonics was frustrated by reversal of the terms of some decision rules so that their first letters spelled the difficult to pronounce nonword unrbcel. The predictor tasks, which we used to predict performance in the placekeeping task, were standard tests of cognitive ability, which have been shown to predict performance differences in a wide range of complex tasks. Inconsistent with the circumvention-of-limits hypothesis, the positive effect of cognitive ability on placekeeping performance did not differ across conditions. This finding adds to previous evidence that it may not always be possible to overcome limitations on cognitive ability through extensive training.