Carly Simon, “Live at Grand Central.”

Carly Simon has had tremendous staying power in the music industry, with her successes and accolades spanning five decades, despite a shyness that sometimes made performing a difficult proposition for her. She’s hesitated to label her condition as stage fright, but she was famously one of the few artists allowed to pre-tape her “Saturday Night Live” appearance. Perhaps her anxiety was lessened by playing unannounced, as she did for a Lifetime TV special filmed at New York’s Grand Central Terminal in April 1995. With no advance hype, commuters were treated to Simon and a full band performing some of her biggest hits. Until recently, this special had been relegated to VHS tapes, but now it’s been digitized and re-edited for release on audio and Blu-ray.

Grammy-winning producer and engineer Frank Filipetti obviously took great care with the remix of this performance. For a concert recorded in the cavernous Grand Central, it doesn’t sound muddy or echoey at all. The instruments are clean and distinct, with Simon’s vocals loud and clear at the top of the mix. The recording now sparkles and properly showcases her gorgeous contralto. Can an artist who’s just been inducted into the Rock and Roll Hall of Fame rightly be called underrated? Perhaps not, but Simon’s work is certainly due for the kind of renaissance Joni Mitchell’s has been having of late. And in that respect, this newly refurbished Grand Central concert has arrived right on time.

The album, now featuring a reordered track list, opens with “Touched by the Sun,” which had just been released in 1994 on her Letters Never Sent album. Carly Simon shows off her incredible vocal control on this song about her friendship with Jackie Onassis. It was Onassis’ idea originally for Simon to perform at Grand Central, to warm up before what was at the time her first tour in 14 years. Simon proceeds to barrel through a nonstop slew of hits: “Anticipation,” “I’ve Got to Have You,” “We Have No Secrets,” “Haven’t Got Time for the Pain,” “Jesse” and her first big hit, “That’s the Way I’ve Always Heard It Should Be.”

“We Have No Secrets” is a revelation, with its jazzy feel and Simon’s jaunty whistling. The track begins with Simon’s between-song banter as she responds to a request for “Jumpin’ Jack Flash.” “Do you really think I’m capable of that?” Simon asks, before singing a few bars. She’s joking, of course, but Grand Central shows that Simon is capable of so much – from low growls to high notes to whistle solos. Simon often brings more emotion to these songs than she did on their original recordings. The country-flavored “Jesse” has far more yearning and desperation that it did on 1980’s Come Upstairs.

There’s a funny moment during the intro to “De Bat (Fly In My Face)” in which Simon explains that the tune from Boys in the Trees (1978), which sounds like a traditional folk song, is based on a true story. One night, while carrying her sleeping child into the dark house, a bat “lost its radar” and flew right into her.

As the tour was supporting Letters Never Sent, the song list leans heavily into that material and includes “Davy,” “Halfway Around the World” and the moving tribute to her mother, “Like a River.”

“Coming Around Again,” one of the strongest songs in Simon’s large and varied repertoire, originally from the soundtrack of 1986 film “Heartburn,” sounds much bigger live, benefitting greatly from the drama of the additional instruments onstage and the strength of the background singers.

The album now ends with “Let the River Run,” Simon’s gospel-tinged anthem from 1989 movie “Working Girl,” a rousing, spiritual ode to New York and its denizens.

Carly Simon is a talented musician and a great communicator. Her songs have been popular throughout five consecutive decades because so many people connected so strongly with them. Fighting past her shyness to perform her songs did not always come easy for her, but when she’s on stage, she’s a dynamic presence, her voice suffused with personality. This new release of Live at Grand Central captures her command of the stage beautifully, and the remixing does it the justice it deserves.

Follow Rachel Alm at Twitter.com/thouzenfold and Instagram.com/thousandfold.