What is the civil partnerships, marriages and deaths Bill
MPs are debating the Civil Partnerships, Marriages and Deaths (Registration Etc.) Bill.
The Bill proposes to see stillborns before 24 weeks are officially registered.
This would give coroners the power to investigate late stage stillbirths and find if there were any problems in prenatal care and deliver - as they can for other deaths now.
And it would bring an end to the current situation when grieving parents who have a stillborn earlier than 24 weeks are effectively told their child ever existed.
The Bill, which was proposed by Tory former minister Tim Loughton, would also allow heterosexual couples to have civil partnerships.
Under current laws only single-sex couples can have a civil partnership - which gives couples the same legal rights as married couples.
But now they can also get married after the law was changed.
Mr Loughton said many straight couples want the opportunity to seal their love with a civil partnership but do not want to get married.
He says the current discrepancy is discriminatory.
The Bill passed its second reading, but will have to return to Parliament to be debated again before it becomes law.