By whom and what songs are played in Remington Steele episode "Steele Trying" DVD release version?

n the 1980's show "Remington Steele" in the 3rd season, episode called "Steele Trying" which can be watched online at this url : http://www.hulu.com/watch/62115/remington-steele-steele-trying#s-p1-so-i0 What song and who sings the song that starts at 5:33 in the show? This is my favorite episode of Remington Steele and have loved the music in it, but I can't figure out the songs nor who sings them. I know it tells the songs were sang by Tony Bennett at the beginning credits, but in the DVD version, I'm not so sure .. I have read online that there was controversy when the show was put on DVD or something and that they didn't want to pay Tony Bennett for the songs. There are other songs throughout the episode and would love to know the name of them all, and who sings them...any help or answers would be GREATLY appreciated !