i have just used ableton to do a mix annd i really had to look hard into it...

the procedure is this:

click the metronome on
pull the track into ableton
pull the first start marker to the absolute start of the 1st beat
'set 1.1 here' then:
'set from here straight'
check a beat near the end of the track and make sure it's spot on...
then work your way through the track ie 17, 33 etc etc, pulling the marker to the right points.... DONT MAKE THEM GREEN.
it should all pull together nice.

if not you're gonna have to try combinations of things... including working through from start to end and making the markers GREEN.. (this is a nightmare, but you can do the whole track like this - it just takes AGES)...

GOOD LUCK!!