Folk music duo Gillian Welch and David Rawlings were frustrated by the quality of vinyl LPs being produced today. So they decided to cut their records themselves.

“What people do nowadays is take a digital file and just run vinyl off that,” says Mr. Rawlings, a lanky musician who plays a 1935 Epiphone Olympic guitar. “In my mind, if we were going to do it, I wanted to do it the way the records I love were made—from analog tapes.”

The Nashville-based singer-songwriters, who gained fame with “O Brother, Where Art Thou” in 2000, spent $100,000 to buy their own record-cutting contraption in 2013. The cutting lathe makes the master copy of a record—the one sent to a pressing plant for mass reproduction. The couple’s first LP, a re-issue of their 2011 Grammy-nominated “The Harrow & the Harvest,” arrives July 28.

Ms. Welch and Mr. Rawlings have gone to extreme lengths to solve a problem many music aficionados say is an open secret in the music industry: Behind the resurgence of vinyl records in recent years, the quality of new LPs often stinks.

Old LPs were cut from analog tapes—that’s why they sound so high quality. But the majority of today’s new and re-issued vinyl albums—around 80% or more, several experts estimate—start from digital files, even lower-quality CDs. These digital files are often loud and harsh-sounding, optimized for ear-buds, not living rooms. So the new vinyl LP is sometimes inferior to what a consumer hears on a CD.