We investigate two approaches to increase the efficiency of phenotypic prediction from genome-wide markers, which is a key step for genomic selection (GS) in plant and animal breeding. The first approach is feature selection based on Markov blankets, which provide a theoretically-sound framework for identifying non-informative markers. Fitting GS models using only the informative markers results in simpler models, which may allow cost savings from reduced genotyping. We show that this is accompanied by no loss, and possibly a small gain, in predictive power for four GS models: partial least squares (PLS), ridge regression, LASSO and elastic net. The second approach is the choice of kinship coefficients for genomic best linear unbiased prediction (GBLUP). We compare kinships based on different combinations of centring and scaling of marker genotypes, and a newly proposed kinship measure that adjusts for linkage disequilibrium (LD). We illustrate the use of both approaches and examine their performances using three real-world data sets with continuous phenotypic traits from plant and animal genetics. We find that elastic net with feature selection and GBLUP using LD-adjusted kinships performed similarly well, and were the best-performing methods in our study.