(CNN) -- Danielle Dayton and Patrick Murray received the call Saturday afternoon: Their 4-pound son, Brayden Murray, was shipping out. Patrick Murray and Danielle Dayton say their tiny son's evacuation went smoothly. As coastal hospitals prepared for Gustav, tiny babies in the Newborn Intensive Care Units were among the first to be evacuated. "The NICU babies are our first priority when it comes to evacuation," said Keith Darcey, a spokesman for East Jefferson General Hospital in Metairie, Louisiana, where Brayden was a patient before being evacuated to Woman's Hospital in Baton Rouge, Lousiana. Woman's Hospital started receiving phone calls Wednesday from coastal-area hospitals inquiring whether there was room in their NICU, spokeswoman Jodi Conachen said. By Sunday evening, the hospital was taking care of 32 evacuated babies.
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Sick newborn babies among first evacuate area, as Gustav approaches
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Touro Infirmary, sent seven NICU babies to Woman's Hospital in Baton Rouge
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"It was very, very, very disorganized," says Touro's chief medical officer
Although Murray said @placeholder's evacuation went smoothly, one hospital administrator said the patient evacuation process had been "incredibly frustrating."