At present, most tools for constructing genetic prediction models begin with the assumption that all genetic variants contribute equally towards the phenotype. However, this represents a sub-optimal model for how heritability is distributed across the genome. Here we construct prediction models for 14 phenotypes from the UK Biobank (200,000 individuals per phenotype) using four of the most popular prediction tools: lasso, ridge regression, Bolt-LMM and BayesR. When we improve the assumed heritability model, prediction accuracy always improves (i.e., for all four tools and for all 14 phenotypes). When we construct prediction models using individual-level data, the best-performing tool is Bolt-LMM; if we replace its default heritability model with the most realistic model currently available, the average proportion of phenotypic variance explained increases by 19% (s.d. 2), equivalent to increasing the sample size by about a quarter. When we construct prediction models using summary statistics, the best tool depends on the phenotype. Therefore, we develop MegaPRS, a summary statistic prediction tool for constructing lasso, ridge regression, Bolt-LMM and BayesR prediction models, that allows the user to specify the heritability model.