The title to By Request made it sound like a number of his earlier LPs, again with the implication that the song choices were made by his audience rather than himself. But where previous records like We Get Letters and Sing to Me Mr. C consisted of old standards (in contrast to the new compositions that made up his single releases), By Request was, for the most part, a collection of recent material. In many cases, Como was borrowing songs associated with his competitors: Jack Jones had just scored a hit with "Lollipops and Roses"; Como's RCA labelmate Elvis Presley had done the same with "Can't Help Falling in Love", from his film Blue Hawaii; Tony Bennett was already popularizing the wistful "Once Upon a Time" from the Broadway musical All American; and Andy Williams had claimed the year's Oscar winner, "Moon River" from Breakfast at Tiffany's. The other tracks included "Maria", newly popular due to the movie version of West Side Story, Rodgers and Hammerstein's "My Favorite Things" from the 1959 musical The Sound of Music, and "The Sweetest Sounds" from Richard Rodgers' new, solely composed show No Strings. Many critics said that the material suited Como especially well, and some even claimed that the singer had made the songs his own. By Request was Como's most successful non-holiday LP release in three years.
A recording of "The Bells of St. Mary's" was made during the sessions, but left off the completed album. It was not released until its inclusion on the compilation CD A Perry Como Christmas in 2001, and "My Favorite Things" is also on, A Perry Como Christmas album.