In February 2006, Super Junior 05 began performances for "Miracle", the second promotional single from their debut album. "Miracle" topped the music charts of Thailand, drawing interest from international markets. As promotions for "Miracle" ended, SM Entertainment began selecting new members for Super Junior's second generation, Super Junior 06. The company even prepared a list of chosen members that were to graduate from the group. However, the company abandoned the rotational concept after adding a thirteenth member, Kyuhyun, in 2006. The group then became known as just Super Junior, without the suffix "05".
After the addition of Kyuhyun, Super Junior released their single "U" for free download on May 25, 2006 on their official website. "U" exceeded 400,000 downloads within five hours of release and ultimately surpassed 1.7 million downloads, crashing the server. The physical single of "U" with a total of three tracks was released on June 6, eventually selling over 81,000 units in South Korea. The single became one of Korea's most popular songs of the year, taking up number one spots for five consecutive weeks on two of Korea's top music programs. By the end of the year, Super Junior collected over seven awards in five of South Korea's top music award ceremonies, and was one of the three Best Newcomer winners at the 21st Golden Disk Awards.
In late 2006, Kyuhyun, Ryeowook, and Yesung formed the subgroup Super Junior-K.R.Y., Super Junior's first sub-unit. They performed their first single "The One I Love", theme song to the Korean television drama Hyena, on the KBS music program Music Bank on November 5, 2006. In February 2007, Leeteuk, Heechul, Kangin, Sungmin, and Eunhyuk formed Super Junior-T, a trot-singing group. They released their first single "Rokuko" on February 23, 2007, and made a debut performance on Popular Songs two days later.
Super Junior's second official album was intended for a late 2006 release, but due to several accidental setbacks, Don't Don was not released until September 20, 2007. Don't Don sold over 60,000 units the first day of release and debuted at number one on the monthly chart of September 2007. Although Don't Don received mixed reviews from critics, the album went to sell more than 160,000 copies by the end of the year, becoming the second best-selling record of 2007. Super Junior received seven nominations at the 2007 Mnet/KM Music Festival, winning three of them which included Artist of the Year, termed by many as the highest recognition of the ceremony. Super Junior collected two more recognitions at the 22nd Golden Disk Awards, including a Disk Bonsang award (Record of the Year).