Selecting a potential father for your children, it turns out, is not unlike shopping online.
"A lot of our clients typically want their donor to be at least 180cm [5ft 11in] tall and have blue eyes," says Peter Bower, director of Nordic Cryobank, who is showing me his database of sperm donors.
Customers narrow their computer search to eliminate men who are under or over a certain weight in kilos.
They can click on a candidate's profile and, for a fee, download an audio interview and a photograph of him as a baby.
Staff also provide a few sentences giving their impression of donors - a physical description or an illuminating detail, Mr Bower says, such as "that he enjoys chatting in the lab after he has donated, dresses nicely or is very interested in a particular sort of music".
But crucially, none of the information will identify an individual, unless he has chosen to be traceable.
In Denmark, sperm donation does not have to come with a name and telephone number - unlike in Britain and in a fast-increasing number of other European countries.
That has made Denmark something of a Mecca for foreign women who want to conceive by artificial insemination, because it has no shortage of officially screened and tested semen.
Danish clinics which provide insemination (often for a fraction of the price of similar treatment in the UK) have three main types of customer: lesbian couples, heterosexual couples and single women. It is the final category which is growing - by far - the fastest.
Peter Bower says single British women are "at the forefront" in choosing this service, but foreign uptake in general is booming. According to the latest figures from the Danish Department of Health, in 2008 2,694 non-Danish women came to Aarhus and Copenhagen for insemination, while in 2010 that number leapt to 4,665.
Samples are delivered from the sperm bank to the aptly named Stork Klinik, across Copenhagen, in the industry's latest gimmick; a bicycle in the shape of a single sperm cell. Deep-frozen in liquid nitrogen, the samples are stored in the spherical head of the sperm, just in front of the handlebars.
Lilian Joergensen is the nurse in charge at the clinic, where women come to be inseminated.
The premises are the epitome of Scandinavian design chic.
"We want the women to feel like queens," she says, pointing to a small wooden crown on the wall above the bed where the insemination is done.
"We hope to create a tranquil atmosphere that will give people a good memory of the place where their baby's story began. Some days we might have 17 inseminations but it's very important to have the same time and attention for every woman.
"We hear her history, her problems, take her mood into account. She must not be a number in a system. She comes here, uses this room as her own, brings a friend, brings candles, whatever she wants."
In their home in New Malden in south London, Kellie Lombard and her partner bear witness to the success of the Danish approach.
Ms Lombard had several expensive but unsuccessful attempts to conceive by sperm donor in Britain and one in South Africa.
She and her partner found out about the Danish option on the internet and now have a family consisting of two mothers, identical twin boys who are nearly five months old, and a girl of two, all fathered by the same anonymous Danish man.
Ms Lombard jokes about the criteria on which their choice of father was based.
"We were originally looking for David Beckham," she says, "but we also wanted someone with lots of academic qualifications."
In fact, they know a surprising amount about the man who is their children's biological father: his age, weight, the fact that he is a medical student, and what he looks like.
Most intriguingly for them, they know what he sounds like as an audio recording was available of him explaining why he was donating - his principal motivation was money - and they thought he sounded like a nice person.
They have now bought up the full legal UK allocation of his sperm. Only a very small number of donations per man are allowed in each country, to limit the chances of half-siblings unknowingly pairing in future.
Ms Lombard's family is an unusual one, she admits. When she takes her extremely Scandinavian-looking daughter to the park, people often ask whether her "daddy" is very tall. Ms Lombard just replies that he is - 6ft 4in, in fact.
If this new European trend in insemination continues, Nordic genes could become more widespread than many would suspect.