Sense of agency (SoA) is the feeling of being the author of given actions and their effects. Recent works have investigated the cue integration approach to agency, according to which different predictive and inferential cues form SoA. In the current research we focus on how two such cues, i.e. accuracy of sensorimotor prediction and prior causal belief, influence SoA measured by temporal binding (TB) and questionnaires. Our results show that whereas learnt action effects produce normal TB and explicit agency, unexpected oddball effects produce enhanced TB but diminished explicit agency. Increased binding was modulated by temporal prediction, but not by identity prediction. A few interpretations of the results are given, including cue integration and pre-activation mechanisms. The research casts new light on the mechanisms and dynamics of TB and adds to the evidence for discrepancies between SoA measures.