Just a few years ago, separation agreements consistently preceded about 7 percent of divorces, providing a cost-effective way for unhappy couples to start dissolving their marriage and a steady source of income for matrimonial attorneys drawing up the agreements.

But in the 3 1/2 years since New York enacted a no-fault divorce statute, the percentage of divorces beginning with a separation agreement has been cut by more than half, even as the number of failed marriages has soared.