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We present a detailed analysis of the systematic errors that affect single-shot carrier envelope phase (CEP) measurements in experiments with long acquisition times, for which only limited long-term laser stability can be achieved. After introducing a scheme for eliminating these systematic errors to a large extent, we apply our approach to investigate the CEP dependence of the yield of doubly charged ions produced via non-sequential double ionization of argon in strong near-single-cycle laser pulses. The experimental results are compared to predictions of semiclassical calculations.