Which visual displays do we aesthetically appreciate, and why? Order and complexity have often been suggested as important factors related to appreciation, but the exact type and direction of their relation to appreciation is still under debate. To disentangle individuals’ aesthetic preferences for order and complexity, it is important (a) to manipulate order and complexity independently and in a parametrically controlled fashion; (b) to study the relation of both factors to appreciation in combination rather than separately; and (c) to acknowledge the multidimensional nature of order and complexity. In a first study, we used the recently developed OCTA toolbox to investigate whether individuals’ preferred complexity levels for color, shape, and size depend on the level of order present in the display. In a 2AFC task, participants (N = 415) indicated their preferences for a series of image pairs, in which complexity levels were varied within each pair, and order levels between pairs. Also, individual differences in preferences for color, shape, and size complexity were explored. Results indicated that (a) not all complexity types are appreciated similarly, (b) not all individuals appreciate complexity equally, and (c) complexity is more often preferred in highly ordered stimuli than in stimuli with a lower order level. A second study examined ratings of order, complexity, pleasantness, and interest for a parametrically controlled set of 1611 stimuli varying systematically in multiple order and complexity dimensions. Results confirmed the differential relation of different types of appreciation to order and complexity, and provide insight in the extent to which some objective order and complexity manipulations influence perceived order and complexity.