Plant morphology influences insect predators' abilities to capture prey and control pest populations. Several mechanisms for this effect of plants on predator foraging have been proposed. In particular, it is often claimed that increased complexity of plant structures may increase search time and reduce foraging success. Using time-lapse photography we recorded search paths, and compared the total path lengths, percentages of plants searched, and path tortuosity of adult multicolored Asian lady beetles (Harmonia axyridis Pallas) and green lacewing larvae (Chrysoperla carnea Stephens) foraging for pea aphids (Acyrthosiphon pisum Harris) on pea near-isolines (Pisum sativum L.) that differed in shape. We found that H. axyridis searched leafy morphologies less thoroughly than those with more branches, while C. carnea larvae search paths did not differ on any of the pea morphologies. In addition, the ability of H. axyridis to attach to plants and maneuver was increased on morphologies with many branches and edges, while C. carnea was able to attach to all morphologies. Both species, however, had significantly reduced predation success on inverted leaf surfaces. We conclude that undersides of leaves, far from the leaf margin, may serve as partial prey refugia. In addition, we find increased plant branching or an increase in other morphological features which provide predator attachment points may promote foraging success.