Genomic selection (GS) is a breeding tool that estimates breeding values (GEBVs) of individuals based solely on marker data by using a model built using phenotypic and marker data from a training population (TP). The effectiveness of GS increases as the correlation of GEBVs and phenotypes (accuracy) increases. Using phenotypic and genotypic data from a TP of 470 soft winter wheat lines, we assessed the accuracy of GS for grain yield, Fusarium Head Blight (FHB) resistance, softness equivalence (SE), and flour yield (FY). Four TP data sampling schemes were tested: (1) use all TP data, (2) use subsets of TP lines with low genotype-by-environment interaction, (3) use subsets of markers significantly associated with quantitative trait loci (QTL), and (4) a combination of 2 and 3. We also correlated the phenotypes of relatives of the TP to their GEBVs calculated from TP data. The GS accuracy within the TP using all TP data ranged from 0.35 (FHB) to 0.62 (FY). On average, the accuracy of GS from using subsets of data increased by 54% relative to using all TP data. Using subsets of markers selected for significant association with the target trait had the greatest impact on GS accuracy. Between-environment prediction accuracy was also increased by using data subsets. The accuracy of GS when predicting the phenotypes of TP relatives ranged from 0.00 to 0.85. These results suggest that GS could be useful for these traits and GS accuracy can be greatly improved by using subsets of TP data.