This paper presents a modified version of the sine wave histogram test for analog-to-digital converter (ADC) characterization. To accurately estimate the transition levels, the input signal has to fulfill strict conditions, which are coherent sampling and uniform distribution of the phases. Noncoherent sampling of the sine wave leads to systematic errors in the transition level estimation, while the nonuniform distribution of the phases increases the variance of the results using the original sine wave histogram test method. The source of the errors is the improper modeling of the histogram of the measured signal. This paper shows that the true histogram of the measured sine wave can be reconstructed by estimating the phases of the sampled signal. It is shown that integrating this information into the estimation of the transition levels can significantly decrease the effect of noncoherent sampling, thus the ADC can be characterized accurately even if the conditions are not fulfilled. The proposed method is verified on both simulated and real measurement data.