Audio pops when starting a new timeline section

I have a video clip with audio in one track, that is broken into segments. When any one segment starts, there is a noticeable popping or crackling noise, regardless of how quiet the audeo might be. Well, maybe the popping noise is related to the volume, but the point is that it is there even when the audio is very quiet.

This happens both when playing the project within Kdenlive, and it also manifests when rendering.

I have tried to counter this by adding one and two frame long audio fades at the beginning and end of video segments and overlapping them in order to create a smooth audio transition, but even with the fades, the audio popping is still noticeable. Regardless of the audio (it's a person talking), one is always made aware that there was a cut there.

Is this a bug, or is there something I can do to make the audio on any one video segment start smoothly without popping or noise?