Centering Music right after the Welcome and Announcements, to settle the congregation into a properly reverential mood;
Meditation, which occurs right after a meditative reading and most of the time is performed immediately prior to the Sermon, and
Offertory, which happens while the Offering is being collected. Typically, this is immediately after the Sermon.
If we have an outside guest musician, he/she/they take these three slots, and because it is a "new face" the congregation willingly accepts pieces which are 3 or 4 minutes' duration. When there isn't a guest musician, and it is the accompanist providing the interludes, the congregational and ministerial time-tolerance decreases by quite a bit. Pieces of more than 90 seconds are frowned upon, and G-d help anyone who dares go over 120 seconds! One time, many years and several ministers ago, I did a 4-minute lute piece, and at about 3 1/2 minutes into it, the minister simply stood up and resumed the service, thereby forcing me to come to an improvised conclusion.
My response was very calm: the next time it was my turn in the cycle, a few weeks later, I played 3 very short elementary etudes, not one of which exceeded 25 seconds!! Since then, and with subsequent ministers, the 75- to 100-second guideline has been adhered to closely. Still, this can be a bit artistically stifling.
So that's how it is in Salt Lake City, but how is this matter dealt with at other congregations??