Several studies have shown that computation of genomic estimated breeding values (GEBV) with accuracies significantly greater than parent average (PA) estimated breeding values (EBVs) requires genotyping of at least several thousand progeny-tested bulls. For all published analyses, GEBV computed from the selected samples of markers have lower or equal accuracy than GEBV derived on the basis of all valid single nucleotide polymorphisms (SNPs). In the current study, we report on four new methods for selection of markers. Milk, fat, protein, somatic cell score, fertility, persistency, herd life and the Israeli selection index were analyzed. The 972 Israeli Holstein bulls genotyped with EBV for milk production traits computed from daughter records in 2012 were assigned into a training set of 844 bulls with progeny test EBV in 2008, and a validation set of 128 young bulls. Numbers of bulls in the two sets varied slightly among the nonproduction traits. In EFF12, SNPs were first selected for each trait based on the effects of each marker on the bulls’ 2012 EBV corrected for effective relationships, as determined by the SNP matrix. EFF08 was the same as EFF12, except that the SNPs were selected on the basis of the 2008 EBV. In DIFmax, the SNPs with the greatest differences in allelic frequency between the bulls in the training and validation sets were selected, whereas in DIFmin the SNPs with the smallest differences were selected. For all methods, the numbers of SNPs retained varied over the range of 300 to 6000. For each trait, except fertility, an optimum number of markers between 800 and 5000 was obtained for EFF12, based on the correlation between the GEBV and current EBV of the validation bulls. For all traits, the difference between the correlation of GEBV and current EBV and the correlation of the PA and current EBV was >0.25. EFF08 was inferior to EFF12, and was generally no better than PA EBV. DIFmax always outperformed DIFmin and generally outperformed EFF08 and PA. Furthermore, GEBV based on DIFmax were generally less biased than PA. It is likely that other methods of SNP selection could improve upon these results.