Early screening for reading difficulties before the onset of instruction is desirable because it allows intervention that is targeted at prevention rather than remediation of reading difficulties. However, early screening may be too inaccurate to effectively allocate resources to those who need them. The present study compared the accuracy of early screening before the onset of formal reading instruction with late screening six months into the first year of instruction. The study followed 164 Danish students from the end of Grade 0 to the end of Grade 2. Early screening included measures of phonemic awareness, rapid naming, letter knowledge, paired associate learning, and reading. Late screening included only reading. Results indicated that reading measures improved substantially as predictors over the first six months of Grade 1, to the point where late reading measures alone provided as much information as the early measures combined. In the light of these results and a less than perfect early screening accuracy, a new strategy for screening is introduced and discussed. The strategy proposes multi‐point screening with gradually increasing sensitivity to strike a balance between manageable screening procedures and outcomes and early identification of students who are most likely in need of extra resources. Copyright © 2017 John Wiley & Sons, Ltd.