This study investigated how rhyme and meter affect eye movements and subjective aesthetic evaluations while reading poems. Earlier findings suggest that the effects might include prosodic predictability-driven cognitive and affective rewards from increased processing fluency (Blohm, Wagner, Schlesewsky and Menninghaus, 2018, McGlone and Tofighbakhsh, 2000), but also semantic and syntactic disfluency, as rhyme and meter are often implemented at the expense of unusual word forms and word order (Menninghaus et al., 2015, Wallot and Menninghaus, 2018). This study set out to investigate the extent to which eye movements might reveal not only distinct effects of fluency and disfluency at the same time, but potentially also hedonic responses that are associated with longer rather than shorter self-motivated exposure, in line with the hypothesis of “savoring” (Frijda and Sundararajan, 2007). The results reveal several fluency-enhancing effects of rhyme and meter on reading times for more global features of the poems, but also increased disfluency effects on gaze durations for some more local features of the poems. Moreover, some of the latter effects are readily interpretable in terms of the savoring hypothesis. Eye movement characteristics that were predictive of higher aesthetic evaluation—irrespective of the presence or absence of rhyme and meter—similarly resulted in increased fluency, disfluency, and savoring effects. Our study thus reveals, for the first time, a complex picture of effects that co-occur while reading poetic prosody, based on analyzing different dimensions of a single psychophysiological variable, namely, eye movements.