This study investigated the relationship between the level of cognitive-linguistic difficulty of task input and the size of the cross-linguistic relationship for academic listening comprehension in emergent bilinguals. It was theoretically motivated by task-dependent cross-linguistic interaction frameworks. We hypothesized that task item sets that involve a higher level of cognitive-linguistic difficulty, drawing on a number of sources of item difficulty, would show a smaller strength of interaction than sets involving a lower level. Using a task-based assessment instrument, listening comprehension was measured in 75 Turkish-Dutch bilingual children at first-grade entry (M[subscript age] = 6;7). Partial L1-L2 correlations indicated that cognitively more demanding item sets tended to coincide with smaller L1-L2 correlations. This finding was, in part, consistent for cognitive difficulty, yet inconclusive for linguistic difficulty. An explanation is discussed that, in line with information-processing theory, highlights a trade-off between cognitive-linguistic task demands and cross-linguistic influence.