Abstract The present study investigated hemispheric processing of puns involving decomposable idioms (e.g. Old skiers never die, they just go downhill) and non-decomposable ones (e.g., Old cleaners never die, they just bite the dust) using a divided visual field paradigm. In two cross-modal priming experiments, participants listened to puns and made lexical decisions for targets presented either in the left or right visual fields. To investigate hemispheric asymmetries at different processing stages (early vs. late), the prime-target inter-stimulus interval was 0 ms in Experiment 1 and was increased to 750 ms in Experiment 2. The results from both experiments demonstrated a left hemisphere advantage for processing puns triggered by non-decomposable idioms; puns motivated by decomposable idioms were processed equally fast in both hemispheres, suggesting that this type of pun induced right hemisphere involvement and led to bilateral processing. We discuss the results in light of predictions derived from the ‘graded salience’ hypothesis and the ‘fine-coarse coding’ hypothesis and argue that the data are more consistent with the graded salience hypothesis.