The principle of optimal design (Rosen 1967) can be stated as follows. `Natural selection leads to organisms having a combination of form and function optimal for growth and reproduction in the environments in which they live.' This principle provides a general framework for the study of adaptation in plants and animals. The efficiency of water use by plants (Slatyer 1964) can be defined as grams of carbon dioxide assimilated per gram of water lost. Leaf temperatures, transpiration rates, and water-use efficiencies can be calculated for single leaves using well-established principles of heat and mass transfer. The calculations are complex, however, depending on seven independent variables such as air temperature, humidity and stomatal resistance. The calculations can be treated as artificial data in a 2N factorial design experiment. This technique is used to compare the sensitivity of the system response variables to changes in the independent variables, and to their interactions. The assumption is made (as a first approximation) that the optimal leaf size in a given environment is the size yielding the maximum water-use efficiency. This very simple assumption leads to predictions of trends in leaf size which agree well with the observed trends in diverse regions (tropical rainforest, desert, arctic, etc.). Specifically, the model predicts that large leaves should be selected for only in warm or hot environments with low radiation (e.g. forest floors in temperate and tropical regions). There are some plant forms and microhabitats for which observed leaf sizes disagree with the predictions of the simple model. Refinements are thus proposed to include more factors in the model, such as the temperature dependence of net photosynthesis. It is shown that these refinements explain much of the lack of agreement of the simpler model. One of the main roles of mathematical models in science is `to pose sharp questions' (Kac 1969). The present model suggests several speculative propositions, some of which would be difficult to prove experimentally. Others, whether true or not, can serve as a theoretical framework against which to compare experimental results. The propositions are as follows. (1) Every environment tends to select for leaf sizes increasing the efficiency of water utilization, that is, the ratio of CO2 uptake to water loss. (2) Herbs are physiologically different from woody plants, in such a way that water-use efficiency has been more important in the evolution of the latter. (3) The stomatal resistance of a given leaf varies diurnally in such a way that the water-use efficiency of that leaf tends to be a maximum. (4) The larger the photosynthesizing surface of a desert succulent, the more likely it is to exhibit acid metabolism, with stomata open at night and closed during the day. (5) In arctic and alpine regions, the plant species whose carbohydrate metabolism is most severely limited by low temperatures are most likely to evolve a cushion form of growth. In addition to providing these testable hypotheses, the results of the model may be useful in other ways. For example, they should help plant breeders to alter water-use efficiencies, and they could help palaeobotanists interpret past climates from fossil floras.