I didn’t realise till now that this song was written in 1926, by Roy Turk and Lou Handman. Here is a lovely old version by Charles Hart, released in 1927.
Elvis recorded it in April 1960 after his Army service. He had spent all day and evening in the studio and it was 4am before he started on the track. He asked for the lights to be turned out and for everyone to leave the studio. After two takes he said to producer Stephen Sholes: ‘Throw that tune out; I can’t do it justice.’ He was persuaded to give it one more go, and that was the one that was released as a single. It topped the charts in both the US and Britain.