The evolution of the vast diversity of floral volatiles is little understood, although they serve fundamental functions, such as pollinator attraction and herbivore deterrence. Floral volatiles are often species specific, yet highly variable and sensitive to environmental factors. To date, nothing is known about the heritability of floral volatiles, and whether individual compounds can evolve independently or solely in concert with the whole volatile bouquet. We conducted bi-directional artificial selection on four target floral volatiles to estimate heritability and correlated pleiotropic responses in the wild turnip (Brassica rapa). The realized heritability of the four target volatiles ranged from 20% to 45%. The average narrow-sense heritability of all 13 analyzed floral volatiles was 18% based on parent-offspring regressions. There were pleiotropic effects of the selected floral volatile compounds on other constituents of the floral scent bouquet, on flowering time and on some morphological traits. We found that the whole floral scent bouquet changed, even when there was selection only on single compounds, with the overall phenotypic covariance being unaffected. Our study demonstrates that floral scent can evolve rapidly under phenotypic selection, but with additional correlated responses in traits that are not direct targets of selection.