I've always preferred artists doing their own interpretations of Elvis songs instead of trying to sound and sing exactly like Elvis did, i.e. being impersonators. One example of the former is Joe Var Veri, a talented artist from Australia that I had the pleasure to discover a couple of days ago.
In fact, it was songwriter Michael Jarrett who pointed me in the right direction by telling me about Joe Var Veri and his new recording of Jarrett's song "I'm Leavin'." Listening to it on the internet, I was impressed with the arrangement that reminded me of Elvis' recording at the same time as it offered a more contemporary sound.
It might come as no surprise that Joe Var Veri is a dedicated Elvis fan himself. Apparently he even made a special trip to Graceland and wrote a song about it. He's also posted a couple of Elvis covers on Youtube with just him and his guitar, among them a nice version of "I'll Be Home On Christmas Day," another great song written by Michael Jarrett.
Returning to "I'm Leavin'" I think it's pretty amazing that a song that wasn't even a hit for Elvis at the time (but certainly deserved to be) nowadays is seen by many fans as one of his best performances. It speaks tons about the quality of the song, and if you listen to "I'm Leavin'" as performed by Joe Var Veri it seems like it could've been written today.