We report an experiment investigating how stimulus complexity and conceptual fluency (i.e., the ease of deriving meaning) influence aesthetic liking judgments for abstract artworks. We presented participants with paintings at two levels of complexity (high vs. low) and five levels of conceptual fluency (determined from a prior norming study) and requested separate ratings of beauty and creativity. Our predictions were derived from the PIA Model (Pleasure-Interest Model of Aesthetic Liking), which views aesthetic preferences as being formed by two, distinct fluency-based processes: an initial, automatic, stimulus-driven, default process and a subsequent, perceiver-driven deliberative process. A key trigger for deliberative processing is assumed to be disfluency at the default stage, as caused by factors such as visual complexity. We predicted that complexity and conceptual fluency would interact in determining aesthetic liking, with people preferring complex stimuli, but only when these are relatively easy to process conceptually. Our results supported this prediction for beauty judgments, although creativity judgments showed a curiously uniform profile. Nevertheless, the predictive capacity of the PIA Model in relation to beauty judgments attests to the explanatory strength of this default–interventionist theory of aesthetic liking. We conclude by noting important parallels between the PIA Model and the Revised Optimal Innovation Hypothesis, which likewise has broad reach in explaining how defaultness and non-defaultness affect pleasure across a range of linguistic and pictorial stimuli.