SYDNEY, Australia — The line goes like this: "You’ve got millions to spare, we only need one."

There is such a critical shortage of sperm donors in Australia that one of the country’s major IVF companies has taken desperate measures — an advertising campaign targeting men’s ‘‘generosity.’’

In Australia, it is illegal to have a commercial (buy or sell) arrangement for human tissue, including sperm, eggs and embryos, so would-be parents rely on donations.

Michael Chapman, a senior fertility specialist with IVF Australia, said that over the past few years, the number of sperm donors had dwindled from over 100 in Australia to less than 30, largely due to changes to the law governing anonymity.

All sperm donors must agree to provide identifying information so that the child can contact them once they reach 18 — a change that has been gradually brought into force over the past three years in all states.

And doctors cannot bring in sperm from overseas that has been donated anonymously. Chapman said that about 15 percent of all sperm donations in Australia came from overseas.

However, some clinics in Australia import up to 80 percent of their sperm supply from the United States, which is legal as long as the person is not anonymous and not paid for supplying the sperm.

IVF Australia only uses local donors because it believes using overseas donors may make it difficult to track down fathers in the future. But it has an 18-month waiting list, which is too long for most women aged over 38, Chapman said.

He hoped the advertising campaign, which is running on major sporting and business websites — and also includes the line ‘‘A donation to us won’t save a life; hopefully it will create one’’ — will reduce the wait to six months.

“I think there are probably men out there …who if they think about it might actually consider it a useful thing to do and take the consequences of loss of anonymity in the future. Men without children [and] in their late 30s might see this as a way of carrying on their gene pool, they might not have thought about it before,’’ Chapman said.

Supply has also been affected by tighter laws governing risk assessments for genetic conditions and diseases.

In the state of New South Wales, the law also required, from January this year, that donors in Australia and overseas be on a register kept by the health department in the same way that it holds information on the HIV status of people.

New South Wales also has far stricter rules. In other states, each donor can provide for 10 families, but in New South Wales, from January, only five families (including the donor’s own), can benefit. This has effectively doubled demand.

There are now only about 10 New South Wales donors.

Sydney clinic Fertility First has been importing sperm from America for the past five years, gradually increasing its supply to between 70 and 80 percent.

The medical director of Fertility First, Anne Clark, said Americans were far more altruistic than Australians when it comes to sperm donation.

FACTS

$1.9 million worth of secretions, including sperm, were imported last year.

Major sources were Britain, the U.S., Canada, Argentina, Denmark and Taiwan.

More than 40,000 Australians accessed IVF services in 2008.

Nearly 11,000 babies were born in 2009 through IVF.

“It’s something they are proud of. It’s not a secret, their families know,’’ Clark said. “How many Australian men do you know of that would be happy to say they’re a sperm donor? These guys are happy to say that. It’s just a cultural difference.’’

She continued: “There’s such a shortage of donors and you don’t know for two weeks if anyone is pregnant so you have to be very careful [not to exceed the five-family rule].’’

She said she has seen a significant drop in Australian donors since anonymity was outlawed but it had not put off Americans.

“We’ve definitely had a decrease in local donors, particularly with this change of legislation in New South Wales. In the last six months I’ve seen 20 men and only one has become a donor.”

She said previously about three or four would have gone ahead.

Although it is against the law to discriminate against lesbian couples, it has been notoriously difficult for them to get access to donated sperm at clinics, due to the shortage.

After being told by a clinic two and a half years ago that it simply does not supply to lesbian couples, one lesbian couple in Brisbane, Queensland, decided to find a donor themselves.

They made contact with a bisexual man on a website and now have a boy, who is two and a half years old.

Even though it was not against the law back then to use an anonymous donor, the couple has maintained a relationship with the man whom they meet up with a few times a year. He also lives in Brisbane and the women also have a close relationship with his parents and two sisters.

One of the mothers, Rebecca, 37, said that they did not pay for the sperm and hoped to have another child using the same donor, who is 52.

He had agreed to have an AIDS test prior to the couple using his sperm, which they injected into themselves at home.

‘‘It was so perfect. It was meant to be,’’ she said. ‘‘It has been a dream run and [the donor’s] family are incredible.’’