The anomalous magnetic moment of the muon, aμ, stands as an enduring precision test of the Standard Model. With the hadronic contribution providing the largest uncertainty to the standing 3.3σ  discrepancy between theoretical and experimental estimates, the combination of e+e−→hadrons cross section data in the determination of ahad, LOVPμ  must be statistically reliable to achieve a precise estimate to aSMμ. Recent studies have highlighted the prospect of systematic biases that can arise through the fitting of global normalisation uncertainties. An analysis of the existing fitting method shows that although it has the potential to incur a bias, previous results are still reliable. However, it is necessary to produce a new, unbiased iterative fitting procedure: the RImmethod. Applying this new method in the determination of the contributions from dominant hadronic channels, plus the inclusion of new precise data in leading channels, provides us with a preliminary indication of the impact on a full analysis of ahad, LOVP μ  .