AbstractDirectional asymmetry is a systematic difference between the left and right sides for structures with bilateral symmetry or a systematic differentiation among repeated parts for complex symmetry. This study explores factors that produce directional asymmetry in the flower ofIris pumila, a structure with complex symmetry that makes it possible to investigate multiple such factors simultaneously. The shapes and sizes of three types of floral organs, the falls, standards, and style branches, were quantified using the methods of geometric morphometrics. For each flower, this study recorded the compass orientations of floral organs as well as their anatomical orientations relative to the two spathes subtending each flower. To characterize directional asymmetry at the whole‐flower level, differences in the average sizes and shapes according to compass orientation and relative orientation were computed, and the left–right asymmetry was also evaluated for each individual organ. No size or shape differences within flowers were found in relation to anatomical position; this may relate to the terminal position of flowers inIris pumila, suggesting that there may be no adaxial–abaxial polarity, which is very prominent in many other taxa. There was clear directional asymmetry of shape in relation to compass orientation, presumably driven by a consistent environmental gradient such as solar irradiance. There was also clear directional asymmetry between left and right halves of every floral organ, most likely related to the arrangement of organs in the bud. These findings indicate that different factors are acting to produce directional asymmetry at different levels. In conventional analyses not recording flower orientations, these effects would be impossible to disentangle from each other and would probably be included as part of fluctuating asymmetry.