The aim of the longitudinal intervention study was to build a model of predictive values of reading fluency in three contrastive reading groups: remedial and computer-assisted remedial reading intervention, and mainstream instruction, to identify the most effective type of intervention for children with different profiles of compromised pre-reading skills. The participants were 7-year-old Finnish school beginners (N = 166). Two remedial interventions took place in four weekly sessions of 45 min over a period of 28 weeks in Grade 1. For a child with deficits in the core pre-reading skills (letter knowledge, phonological awareness or rapid automatized naming), the computer-assisted remedial intervention would be the most successful in remediating reading fluency in the transparent Finnish language. Furthermore, children in the computer-assisted intervention were able to reach the average level of the mainstream children by the end of Grade 2. (Contains 2 tables and 2 figures.)