Ignoring irrelevant visual information aids efficient interaction with task environments. We studied how people, after practice, start to ignore the irrelevant aspects of stimuli. For this we focused on how information reduction transfers to rarely practised and novel stimuli. In Experiment 1, we compared competing mathematical models on how people cease to fixate on irrelevant parts of stimuli. Information reduction occurred at the same rate for frequent, infrequent, and novel stimuli. Once acquired with some stimuli, it was applied to all. In Experiment 2, simplification of task processing also occurred in a once-for-all manner when spatial regularities were ruled out so that people could not rely on learning which screen position is irrelevant. Apparently, changes in eye movements were an effect of a once-for-all strategy change rather than a cause of it. Overall, the results suggest that participants incidentally acquired knowledge about regularities in the task material and then decided to voluntarily apply it for efficient task processing. Such decisions should be incorporated into accounts of information reduction and other theories of strategy change in skill acquisition.