Adding an upright inner square frame to an outer tilted square frame causes a central rod's perceived orientation to be directionally opposite the usual rod-and-frame illusion (RFI). Zoccolotti, Antonucci, Daini, Martelli, and Spinelli (1997) attributed this double RFI (DRFI) to Rock's (1990) hierarchical organization principle. In Experiment 1, this explanation predicted results for small (11°) but not larger (22° and 33°) outer frame orientations. In two experiments with the DRFI, bottom-up, goal-driven attention was varied and direct and indirect measures of the framework's influence were compared. In Experiment 2, the RFI angular function was compared with two other DRFI conditions: a direct measure of perceived rod orientation and an indirect measure of the inner frame. These conditions induced directionally opposite effects. In Experiment 3, direct and indirect measures of the inner frame's perceived tilt were compared. Angular functions differing in size and direction were obtained. Experiment 4 replicated the previous results, using a different psychophysical procedure. All the results were consistent with the hierarchical organization mechanism but suggested different processing strategies due to different attentional weights. They were also consistent with other recent findings based on the Bayesian approach to accounts of illusory phenomena (e.g., Jazayeri & Movshon, 2006, 2007; Weiss, Simoncelli, & Adelson, 2002).