In a randomized-controlled trial we tested a computer-assisted intervention for the prevention of reading difficulties, delivered by nonprofessional tutors, running from kindergarten to halfway Grade 2. The full sample included 123 prereaders (M = 5; 6 years; 56 intervention; 67 controls) with low preliteracy skills. Parents were sent a questionnaire to assess family risk (FR) for reading difficulties. There was no intervention effect in the full sample, but, unexpectedly, the effect differed between subsamples that did and did not return the questionnaire. The intervention did not affect reading acquisition in the subsample (N = 49) without FR-data, mostly children from immigrant, non-Dutch speaking, low-socioeconomic status (SES) families, but had large effects in the subsample of Dutch-speaking, middle and high SES-parents with FR-data (N = 74). The latter subsample was followed until Grade 6, 4 years after the intervention, and included 36 intervention children and 38 controls. Long-lasting improvements were found in word-reading fluency, which transferred to reading fluency for pseudowords, English words: and texts, and to spelling. The intervention substantially reduced the need for remedial teaching and grade retention. On all measures, children with FR performed worse than children without FR. The intervention had similar effects on the progress of both groups, but the FR children needed more sessions. This study shows that a 2-year cost-effective early intervention can reduce the incidence of reading difficulties. However, it remains a challenge to make the intervention suited for children in which a lack of preliteracy skills merely seems to reflect a lack of learning opportunities.