The first time Thomas Newman watched “The Shawshank Redemption” wasn't a wholly enjoyable experience. The composer had been chosen to write the score for the film, and as the screening at the old Warner Hollywood lot concluded, he felt a mix of joy and despair. “How could you not make this a worse movie?" he recalls thinking.

Mr. Newman didn't make “Shawshank” worse. After a disappointing theatrical release in September 1994, the film took off on home video and cable and became one of the most popular movies of the past 20 years. “Shawshank” earned Mr. Newman the first of 12 Academy Award nominations for films including “American Beauty,” “Wall-E” and “Saving Mr. Banks.”

The enduring cultural and economic power of “Shawshank” was the subject of a recent article in The Wall Street Journal, and after its publication some wondered how we could run such a piece without mentioning the contributions of Mr. Newman. On the eve of the 20th anniversary of the film’s release, we reached out to the 58-year-old composer, who shared his thoughts about the movie and how it shaped his future work.

Mr. Newman says “Shawshank” elicited such strong emotions without any music at all that the challenge was to create a score that elevated scenes without getting in their way. When he brought director Frank Darabont to his studio to walk him through an early version of his work, striking that delicate balance soon emerged as a focus of their collaboration.

“Shawshank Redemption,” the piece playing during Andy Dufresne’s escape, starts slowly and gathers speed as it builds toward the climactic moment when Tim Robbins’ Andy emerges from the sewage pipe, strips off his clothes and raises his arms toward the sky as rain washes over him. But the piece in the movie is a slightly toned-down version of the original cue. Mr. Darabont preferred a one-note climax over Mr. Newman’s three-note motif. “The crescendo of the music there felt too big to me, it had too much of a triumphal flourish,” says Mr. Darabont. “I asked Tom to dial it back a few degrees.”