Producer Ben Frost, whom Stetson had previously worked with on "New History Warfare Vol. 2: Judges", mixed between fifteen and twenty recordings of the same performance into a cohesive piece of music at Greenhouse Studios in Iceland. The vocals of Justin Vernon were recorded at April Base studios in Fall Creek, Wisconsin, and were overdubbed later in the recording process. "New History Warfare Vol. 3: To See More Light" contains eleven tracks with a total running time of fifty-two minutes. Ten tracks were written by Stetson, with three of these featuring additional writing from Justin Vernon. The track "What are They Doing in Heaven Today?" is a cover version of a gospel song written by Charles Albert Tindley in 1901 and recorded by Washington Phillips in 1928. Stetson has stated that the songs are "based in traditional American song," and the music was described by AllMusic reviewer Fred Thomas as containing "elements of jazz, modern composition, and... aspects of repetition and textural drone found in certain branches of electronic music and noise." "Fact" called the album "a rich, multi-layered sonic world" and noted that the presence of Vernon's vocals meant that "Stetson’s approach feels considerably poppier this time around." Pitchfork Media opined that Stetson has "plowed a unique path through the music landscape in the last five years," stating that "his music is heady but always rooted in the body." Jeremy D. Larson concurred with this idea, claiming that Stetson's music is "alien but human, technically astounding but filled with passion – the saxophone acts as a medium of expression tied to his whole body", but admitted that "to most ears, Stetson’s music is hard to classify." Reviewer Daniel Paton also found classification of the music difficult, saying that it "doesn’t really meet even the most open-minded definitions of jazz, neither is it really an example of free improvised music." In his review for Drowned in Sound, Alexander Tudor observed the album's "abrasiveness, brute force, and determination to push the instrument to its limits," describing a "relentless pummelling of metal in motion; often aggressive or chaotic, but using scales to evoke a sense of discipline" while noting that Stetson was "equally at home with classical minimalism." "Exclaim!" reviewer Vincent Pollard noted how "Vol. 3" "organically and coherently blends Stetson's avant-garde playing and dark, complex themes with accessible and compelling compositions," while MusicOMH commented that Stetson was "finding guttural, fuzzy, violent sounds from his saxophone... but also finding a disarming warmth where necessary."