Like on a track, the lingering chord from the last song would be at the very beginning.

Sometimes they can't help that, because CD track indices must fall one 1-second boundaries. So if the two are really close together, sometimes they have to make a choice between letting a split second of the prior song appear, or cutting off a split second of the next song.

Of course, if you're talking about ones where there's a long lull between the songs and the engineer was just sloppy, then yeah that's irritating.

One thing I particularly hate is the habit of indexing a live CD so that the artists' "talking introduction" is at the end of the prior track instead of at the beginning of the track it goes with. Makes shuffles really suck: "I'd like to play a song for you that I wrote about the sweetest girl I ever knew. Jenny, this one's for you..." <BZZT> NIN's "Closer" plays instead.

Occasionally, I've deliberately done some cutting and pasting of the rips to put the intros properly onto the song they're supposed to go with. But boy what a pain in the ass.
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Tony Fabris