Competitive methods for irregular oscillatory integrals were extended by multiple quadrature cases. Some work used α-dense curves to convert multiple quadrature rules into oscillatory quadrature in one dimension. There was scope to apply the generalised approach to the resulting integrals. The original authors used a sledge hammer approach to their final quadratures and in this paper a more efficient approach to integrating the resulting one dimensional integrals is made. In the process, errors in the original paper have been uncovered and corrected. The original authors obtained what appears to be rapid convergence to what are unfortunately the wrong values. The outcome is that an assessment is made of the viability of using dense curves in this way, and getting the correct results in both two and three dimensions.