 This study presents a detailed analysis of systematic errors affecting single-shot carrier envelope phase, CEP, measurements in long acquisition time experiments with limited laser stability, and proposes a scheme to eliminate these errors. The approach is applied to investigate the CEP, dependence of doubly charged ions produced via non-sequential double ionization of argon in strong near-single-cycle laser pulses, comparing experimental results to semi-classical calculations. This article was authored by M. Kubel, K. J. Bech, Nora G. Johnson and others.