Apple Logic Pro /LogicExpress Discussion

I'm having  a devil of a time editing out unwanted silence at the end of mp3 tracks 
bounced from a Logic sequence.  I find that if the end point of the bounce is too close to 
the end of the audio, there occurs an echo/spike  that ruins the silence at the end of the 
track.  This happens even if the audio has reached a silent state.  it all depends on how 
much time is allowed between the end of sound and the bounce end point.  

I work in the theater where it is necessary, for theatrical audio cues to not have extended 
track time at the end of each track.  Yet adding silent time to the bounce seems to be the 
only way to avoid the 'spike'.  Funny, the spike is not heard when Logic plays the track if 
it's imported back into the program (and indeed, the 'echo' is not even visible in the audio 
track editor), yet, when it is played externally as a bounced .mp3 by software such as 
Quicktime or iTunes, the unwanted echo almost always happens if the cut-off comes too 
quickly. Does anyone know of this problem and are there any solutions available?

Btw, this is occurring in offline bouncing.  Haven't tried it in real time yet - that just may 
be the work-around, but I do prefer the offline method.

Much obliged,

Michael S.