Cassava (Manihot esculenta Crantz) is a clonally propagated staple food crop in the tropics. Genomic selection (GS) reduces selection cycle times by the prediction of breeding value for selection of unevaluated lines based on genome-wide marker data. GS has been implemented at three breeding programs in sub-Saharan Africa. Initial studies provided promising estimates of predictive abilities in single populations using standard prediction models and scenarios. In the present study we expand on previous analyses by assessing the accuracy of seven prediction models for seven traits in three prediction scenarios: (1) cross-validation within each population, (2) cross-population prediction and (3) cross-generation prediction. We also evaluated the impact of increasing training population size by phenotyping progenies selected either at random or using a genetic algorithm. Cross-validation results were mostly consistent across breeding programs, with non-additive models like RKHS predicting an average of 10% more accurately. Accuracy was generally associated with heritability. Cross-population prediction accuracy was generally low (mean 0.18 across traits and models) but prediction of cassava mosaic disease severity increased up to 57% in one Nigerian population, when combining data from another related population. Accuracy across-generation was poorer than within (cross-validation) as expected, but indicated that accuracy should be sufficient for rapid-cycling GS on several traits. Selection of prediction model made some difference across generations, but increasing training population (TP) size was more important. In some cases, using a genetic algorithm, selecting one third of progeny could achieve accuracy equivalent to phenotyping all progeny. Based on the datasets analyzed in this study, it was apparent that the size of a training population (TP) has a significant impact on prediction accuracy for most traits. We are still in the early stages of GS in this crop, but results are promising, at least for some traits. The TPs need to continue to grow and quality phenotyping is more critical than ever. General guidelines for successful GS are emerging. Phenotyping can be done on fewer individuals, cleverly selected, making for trials that are more focused on the quality of the data collected.