Two studies assess French-speaking children's comprehension of object filler-gap dependencies, with the goal of investigating whether the degree of specificity/set-restriction of the fronted object or the intervening subject modulates comprehension. We tease apart the predictions of various accounts attributing children's difficulties to (i) similarities between the object and the intervening subject (Gordon et al., 2001, 2004), particularly when both constituents share a structural +NP feature (Friedmann et al., 2009); (ii) increased processing cost determined by an operation of set-restriction (Goodluck 2010); and (iii) the tendency to incrementally interpret sentences and the subsequent difficulty in revising an early commitment to an agent/subject-first analysis (Trueswell et al., 1999). Our results support the incremental processing view as they reveal that only a less specific fronted object, but not a less specific intervener, enhances comprehension. This suggests that referentially ambiguous objects alleviate children from an erroneous initial interpretive commitment to an agent/subject-first structure.