Fertility treatment is far more likely to result in multiple births than natural conception.
Twins, triplets and other multiple births also increased over the decade, partly due to fertility treatments.
Death, job loss, divorce, multiple births and a broken marriage engagement all qualify for the break.
This has become more common since 2001 with more than 16 in every 1, 000 deliveries now involving multiple births.
Some kind of system is a must, says Sarah Newell, sponsorship manager of the Twins and Multiple Births Association, Tamba.
Multiple births tend to lead to smaller babies, and a higher risk of health problems for both the babies and their mother.
But the same does not apply to parents who have multiple births.
Caveat: The study excluded multiple births, which are associated with increased risk of developmental problems, limiting the findings to single gestations, researchers said.
Putting only one fertilised egg into the womb avoids multiple births, which are known to increase the health risks of both mother and child.
The Twins and Multiple Births Association (TAMBA), which offers support to the parents of twins and triplets, has already expressed concern about any changes.
Dr Nygren said the natural rate of multiple births was around 1%, but was between 20% and 40% for women who used assisted reproductive techniques.
But the Twins and Multiple Births Association reacted angrily to the proposals saying they flew in the face of what most patients and doctors wanted.
Rich urbanites are increasingly willing to pay the fines, or sometimes even buy expensive in vitro fertilisation treatment that might increase their chances of having multiple births.
Carrie Jones said Monday she had been using injections to help her conceive, but the couple did not undergo in vitro fertilization, which sometimes results in multiple births.
Multiple births, a consequence of implanting more than one embryo to increase the odds of success, are one of the biggest risks associated with IVF for both mother and child.
BBC: IVF should be given sooner and to older women, says NICE
Lead researcher Professor Geoffrey Sher said the test may allow doctors to cut the number of embryos they use in IVF treatment - and thus reduce the number of multiple births.
It opens up the prospect of selecting high-quality embryos to replace into the womb, increasing success rates, reducing the financial and emotional cost to patients and greatly eliminating the risk of multiple births.
Keith Reed, chief executive of the Twins and Multiple Births Association (TAMBA), said any decision to avoid a blanket ban on the use of more than one embryo represented a "victory" for patients.
With multiple births increasing the risk of premature delivery, the possibility of a caesarean and the chance deformities and disabilities, UK clinics were last year directed not to return more than two embryos to a patient's womb.
The number of multiple births in the UK was low - only just over a quarter of pregnancies resulted in more than one baby, whereas nearly half the successful fertility treatments in Spain resulted in a multiple delivery.
One concern expressed by many in the field is that the number of multiple births has increased in recent years - the chances of parents having IVF triplets rose from one in 200 to one in 20 during the 1990s.
Comparing the figures released by ESHRE with those in the US is difficult, because of differences in the way they are calculated, but broadly, the US has higher "success" rates in terms of live births, but also a percentage of multiple births which is higher than the European average.
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