(FORTUNE Magazine) – Will the world's Catholics dig deeper to help the Vatican? If so, they will be following the example of a tiny rural diocese in the American Midwest whose members are among the world's most generous contributors to the Holy See. Bishop John J. Leibrecht, 57, shepherds the diocese of Springfield-Cape Girardeau, which takes in the southern part of Missouri, from Springfield in the west to the Mississippi River town of Cape Girardeau. The diocese's 39 counties include ten of Missouri's poorest. This is fundamentalist Protestant country, and practicing Catholics number only 50,000 out of a population of one million. Officially Springfield-Cape Girardeau is listed in the Vatican's register as a ''mission'' diocese that depends on outside funds to keep going. But its contributions to last year's Peter's Pence collection averaged $1.50 for every man, woman, and child. Though modest, that exceeds the U.S. average of less than $1. The worldwide figure is a fraction of that. At the same time, the members support an active and growing diocese with 91 churches and missions, 22 elementary schools, three high schools, and seven hospitals. Bishop Leibrecht has made progress against the fiscal woes of his diocese. The deficits have come down from $214,581 in fiscal 1986 to an estimated $48,946 this year on total expenditures of $2.3 million. He is looking forward to a balanced budget in fiscal 1988. A firm believer in accountability, Leibrecht practices the kind of financial disclosure that the Vatican is just getting around to. His flock gets a full annual statement, and last month he had the pleasure of announcing that ''our spiraling deficit has been contained. That was not easy!'' When asked for details, the soft-spoken bishop mentions increased donations from parishoners, more outside help from mission societies around the U.S., and ''belt-tightening.'' Making ends meet is not easy, he says, because the schools are overwhelmingly staffed by lay teachers, who cost more than priests and nuns. The latter also get salaries, and Leibrecht adds: ''We have to provide pensions for them and house them. Because we have such a wide geographical expanse, just keeping them in cars is a problem.'' Financial headaches have not stopped the people of Springfield-Cape Girardeau diocese from attacking the same social problems that confront major metropolitan areas. Last year the diocese helped start the Missouri Hotel for the Homeless. With 300 volunteers, the hotel feeds and cares for hundreds who are, in the bishop's expression, ''down on their luck.'' It is considered one of the most successful such efforts in the nation. Pressed to explain why his diocese provides outsize support to the Pope, Bishop Leibrecht explains: ''Maybe it has to do with his charisma as he visits and our people get to see him, on television if not in person. Maybe it has to do with their minority position in Missouri. They appreciate being part of the larger Church.''