A substrate is loaded onto a substrate support of a lithographic apparatus, after which the apparatus measures locations of substrate alignment marks. These measurements define first correction information allowing the apparatus to apply a pattern at one or more desired locations on the substrate. Additional second correction information is used to enhance accuracy of pattern positioning, in particular to correct higher order distortions of a nominal alignment grid. The second correction information may be based on measurements of locations of alignment marks made when applying a previous pattern to the same substrate. The second correction information may alternatively or in addition be based on measurements made on similar substrates that have been patterned prior to the current substrate.