A few years ago, the congregation switched to the wheat wafer the Cavanaghs make from the white.

“There’s a nice clean bread flavor, as opposed to the paste flavor you have with some other breads,” Mr. Dietel said.

Image Some customers say the Cavanaghs have such a big market share because their product is about as close to perfect as earthly possible. Credit... Jodi Hilton for The New York Times

His congregation buys about 6,000 wafers a year from a Seattle religious goods store. Traditionally, nuns, priests or members of a congregation baked altar bread. (In the Catholic tradition it is unleavened and contains only flour and water; other denominations, including Southern Baptists, allow the use of additional ingredients.)

In 1943, Andy’s great-grandfather, John Cavanagh Sr., an inventor, and grandfather, John Jr., were asked to help local Catholic nuns renovate their antiquated baking equipment. The men created ovens and mixers for the nuns; then three years later, John Jr. and his brother Paul started making bread themselves.

They distributed all of it to Catholic churches and monasteries.

The Cavanaghs are Catholic and John Sr. let his sons run the business so he could concentrate on his first love, liturgical art. Crosses and paintings are showcased in a room in the Rhode Island offices.

For about 20 years, the Cavanagh bread was small, white and nearly transparent, intended to melt on the tongue. After the changes initiated in the church at the Second Vatican Council in the 1960s, Catholic churches wanted the wafers to be thicker and chewable, like real bread.

The Cavanaghs started producing the wafers of today  usually whole wheat and sealed on the outside to prevent crumbs.

In 1970, Paul’s sons, Brian and Peter, joined the business and started expanding the company’s reach beyond New England and the Catholic Church, where fewer and fewer nuns were making bread.