One of the crucial questions which high energy elastic data ought to be able to answer is: is the odderon contribution really necessary? Using a model with mildly energy dependent form factors as input and performing full eikonalization before we compare with the data, the answer that we find from a careful examination of the various options is that the odderon is indeed necessary if: 1) we trust the ISR pp data to be precise enough that their comparison with the collider data on ppBAR is meaningful, 2) we demand quantitative (i.e. not just qualitative) agreement between theory and experiment and 3) we account for the large \t\ data.581109117