Pink and her motocross racer hubby Carey Hart say they had their childbirth all planned out. The couple welcomed their first child, Willow Sage, June 3 in Los Angeles, California. Pink and Carey originally planned to have their baby girl naturally. She wanted to give birth while "perfectly present, unmedicated, in the way nature intended,” the singer told PEOPLE.

Turns out baby Willow had plans of her own. “She was in the frank breech position, which is head up with her legs up by her head in a pike position. We tried everything to turn her around,” but after two nights of labor Pink decided to go for a Cesarean section.

Though she would have rather had her baby the natural way, Pink was relieved that Willow is happy and healthy and that she will “go for your natural birth next time, for sure.”

Pink and her husband thought long and hard about Willow’s name. The Grammy winner said that the willow is her favorite tree and that it is the most flexible tree in nature and that nothing can break it. Pink continues, “Sage is cleansing and sacred. And it sounded great together.”