In order to test early-generation selection for grain quality, random F1-derived progeny from a multiple convergent cross of 16 high-yielding bread wheats were grown in F3 generation, along with the parents, as spaced plants in a glasshouse under optimal conditions. Progeny lines were then advanced without selection to F7 when 58 random lines were sown with the parents in a replicated yield experiment at Griffith under irrigation and optimal management. Small-scale grain quality tests were performed on grain from the F3 plants, the F7 plots and the parents. The tests comprised particle size index (PSI), grain and flour protein content (GP, FP), sodium dodecyl sulfate sedimentation volume (SDS), Pelshenke wheatmeal fermentation time (PEL) and flour milling yield (MY). There were significant genotypic effects for all quality traits in each generation. Phenotypic correlations in F3 and in F7 showed positive correlations between protein content and SDS and PEL, and in F7 a strong negative correlation between grain yield and grain quality (GP, FP, SDS, PEL). Across generations (F3 versus F7), the relationship was strong for PSI, moderate for SDS and PEL, but nonsignificant for the other traits. The realized heritability was high for PSI (77%), moderate for SDS (44%) and PEL (47%), but low (18-24%) in the other cases. Selection at an intensity of 26% for the first three mentioned traits did not significantly change grain yield, plant height or flowering date, although for GP and FP it did lower grain yield by 7%. Desirable quality types were defined within the three hardness (PSI) classes, namely, hard, intermediate, and soft (gluten type not biscuit type). Retrospective selection in F3 for desirable types significantly and markedly increased the frequency of desirable types in each class by three- to eight-fold. It is concluded that in wheat early generation selection for PSI, SDS and PEL, even when practised upon glasshouse-grown plants, gives useful progress without prejudicing grain yield.