In a letter from Colonel Parker to Elvis, dated August 6 1957 (see below), it appears that 'One Night' was planned to be re-recorded at these sessions.

It may have also been at these sessions that Elvis tried to record 'Fools Hall Of Fame'. At concerts around this time it is said Elvis announced that 'Fools Hall Of Fame' would be his next single (it is known Elvis sang the song in Vancouver, Canada on August 31, and also in Seattle, Washington on September 1 1957), and is noted as such in the book Day By Day (Ernst Jorgensen and Peter Guralnick) on page 110.

In an interview with D.J. Fontana by Arjan Deelan, published on the Elvis Information Network in August 2010, D.J. mentions 'Fools Hall Of Fame' and the relevant part of the interview is duplicated below:
Q: It's been said that Elvis announced 'Fool's Hall Of Fame' as his new single. Does that ring a bell?
Fontana: We tried that tune, I guess half a dozen times. I don't remember if we ever got a good cut. We tried it. On stage it was great. I think he finally cut it.
Q: You tried it in the studio?
Fontana: Yeah, but there was something about it, It was just one of those songs that you can't get a feel on. I think they finally cut it, but it was a throwaway song, and that's why it was never released. It'll probably come up, somebody will find it and release it. RCA or somebody and then we'll sue them again! (laughs)

It is possible that they ran through 'Fools Hall Of Fame' at these sessions but never got further than the rehearsal stage, either that, or they never recorded a satisfactory take and the tape was erased. As the tapes from these sessions are missing (or were erased by RCA in the 1959 vault clean out) it is impossible to know, but this theory should not be discounted.

The re-recordings of 'Oh Little Town Of Bethlehem', 'Santa Bring My Baby Back (To Me)', 'Santa Claus Is Back In Town' and 'I'll Be Home For Christmas' can found on the 2017 album Elvis: Christmas With The Royal Philharmonic Orchestra, which contained Elvis' original vocals but with new backings by The Royal Philharmonic Orchestra.

In March of 2007, Sony decided to go through all of Elvis' masters. They retransferred everything and remastered all tracks including repairing as many clicks, pops, bad edits and dropouts as they could. They have used these newly mastered recordings on their new releases since 2007 including budget soundtracks, Legacy releases, the 30 disc Complete Elvis Presley Masters collection and the Franklin Mint package.

Thanks to Kevan Budd for research on 'Fools Hall Of Fame'.