In recent years, several studies have reported beneficial effects of transcranial alternating current stimulation (tACS) in experiments regarding sound and speech perception. A new development in this field is envelope-tACS: The goal of this method is to improve cortical entrainment to the speech signal by stimulating with a waveform based on the speech envelope. One challenge of this stimulation method is timing; the electrical stimulation needs to be phase-aligned with the naturally occurring cortical entrainment to the auditory stimuli. Due to individual differences in anatomy and processing speed, the optimal time-lag between presentation of sound and applying envelope-tACS varies between participants. To better investigate the effects of envelope-tACS, we performed a speech comprehension task with a larger amount of time-lags than previous experiments, as well as an equal amount of sham conditions. No significant difference between optimal stimulation time-lag condition and best sham condition was found. Further investigation of the data revealed a significant difference between the positive and negative half-cycles of the stimulation conditions but not for sham. However, we also found a significant learning effect over the course of the experiment which was of comparable size to the effects of envelope-tACS found in previous auditory tACS studies. In this article, we discuss possible explanations for why our findings did not match up with those of previous studies and the issues that come with researching and developing envelope-tACS.