Seeking to expand their family trees, thousands of amateur family historians have begun asking people with the same last names to compare genes, even though most are total strangers. That is where the free drinks come in.

"I always say, never ask for DNA on a first date," said Georgia Bopp, 65, a retired banker in Kailua, Hawaii. "A courtship is involved."

Bopp woos with family tree diagrams from Web sites like Ancestry.com. Only after several e-mail exchanges does she mention DNA, and then she is quick to clarify that the test does not involve needles.

But when a detour on a recent trip brought her within miles of the only living male descendant of her maternal great-grandfather, she went for the direct approach. Determined to get the purest sample, she grabbed his glass at a local restaurant before the waitress filled it.

"Have you had anything to eat or drink in the last hour?" Bopp asked, whipping out the DNA kit stashed in her purse.

"She wanted my saliva, basically," said Warren Lenhart, 60, a foreign policy analyst whose test confirmed that they both had descended from a man who emigrated to Philadelphia from Germany in 1748. "There was no time for small talk."

DNA genealogy tests hold out new hope for adoptees like Paul Gilbert, 77, of Los Angeles. Searching for his biological relatives, Gilbert uncovered his birth mother's name in records, which pointed him to a man he believed to be his half-brother. But the man was not eager to verify it through a DNA test. "I can't imagine my father consorting with a woman like that," he wrote to Gilbert of his mother.

When the man finally came around, Gilbert, a retired lawyer, was just as glad that there was no genetic match. "He didn't sound very nice," he said.

Since learning that she shares some markers with St. Luke the Evangelist, Kathy Johnston, 54, a dermatologist in Torrance, Calif., has been lobbying to have the saint's remains more thoroughly analyzed.

She believes St. Luke's mother was Celtic, as is her own lineage, not Syrian, as previous genetic tests on remains in Padua, Italy, have suggested. She is willing to pay for the test, but scientists at the University of Ferrara and the Roman Catholic Church have ignored her theories.

The basic tests are sold for $99, a small fraction of what they might have cost a decade ago. But test 40 relatives, and costs can add up.

To her husband's dismay, Melissa Robards, nee Springer, has spent more than $1,000 testing Springers around the country to see if they are related. She has been known to send flowers to stubborn holdouts.