You may not have been aware of this, but recently the country of Canada was considering whether to eliminate its infanticide law.
As reported in the Montreal Gazette, Ontario's top court ruled that "a woman who kills her newborn baby can continue to use infanticide resulting from postpartum depression as a defense against the charge of murder."
Whereas a murder charge could lead to a life sentence, a conviction of infanticide in Canada carries a maximum 5-year sentence. It would apply to any mother who, "… through a 'willful act or omission' causes the death of a newborn under 12 months because 'her mind was disturbed. following childbirth or lactation."
The Gazette story stated that the Crown asked the court to revisit the infanticide defense "… last September after a 29-year-old woman was found guilty by a trial judge of infanticide for killing two of her babies. She ended up spending one year in prison after being given credit for pre-trial custody." The government felt the infanticide law was outdated and no longer reflected the views of society, as apparently neither the prosectors nor the public was happy with the amount of this woman's prison time.
The US doesn't have such laws, but I believe they are common in Europe. Texas was attempting to be the first state to enact an infanticide law, but I don't believe that has happened.