Vague description, but maybe someone will know

This was an English-language adult contemporary pop song that came out sometime in the late 1970's or early 1980's. The vocalist was male. It is still played now and then on pop and A/C stations, so it isn't all that obscure. It must have been something of a hit. I guess the genre would be adult contemporary/romantic.

This was a saxaphone-driven song. I'm not sure if the chorus itself was a wordless saxaphone line, but the song did have a prominent sax line that was repeated several times. It was a fairly slow, relaxed sax line. I'm not a musician, but it sounds like a tenor sax. The notes were not played particularly high or low-pitched.

The vocalist sounds like Gerry Rafferty. However, I went though the sound clips on Rafferty's 'Greatest Hits' album and none of them matched. This song is NOT 'Baker Street.' To give you a point of reference, the notes on Baker Street are played higher and faster than the notes in the song I am thinking of. I can also tell you that the vocalist is not James Taylor.

I don't remember any of the lyrics, since the lyrics are delivered in a fairly soft tone. This is a slow-sax-driven song.

Just first one that came in my mind: Rick Springfield - Don't Walk Away

YouTube - Rick Springfield - Don't Walk Away -1984 (Solid Gold)

And now I remembered another one, Glenn Frey - You Belong To The City

YouTube - Glenn Frey - You Belong To The City

Thanks for the reply. The songs you mentioned aren't the particular one I'm thinking of, but they are useful as points of comparison. The Glenn Frey song has a quicker tempo and more instrumental activity than the song I'm thinking of. In fact, I can't think of a moment in that song where the vocalist gets very excited. However, the pitch of the sax is close.

The Rick Springfield song is much more lively and up-tempo, too. The song I'm thinking of really does sound like a fleshed-out version of a generic elevator music tune.

I'm guessing that if it was Dire Straits you would have remembered.
Anyway, try this on the off chance:
YouTube - Dire Straits - Your Latest Trick