We recently attended a birth which had interesting conditions of the placenta. Here are some pictures of a circumvallate placenta with velamentous insertion of the cord.
In 99% of pregnancies, the umbilical cord inserts on the placental mass. The insertion site may vary from the center of the fetal surface to the border of the placenta. The term velamentous insertion describes the condition in which the umbilical cord inserts on the amniotic membranes rather than on the placental mass. Therefore, a segment of the umbilical vessels runs between the amnion and the chorion of the amniotic sac, losing the protection of the Wharton's jelly.

The incidence of this condition is about 1.1% in singleton pregnancies The most significant problem arising from a velamentous insertion of the umbilical cord is vasa previa, a condition in which the velamentous umbilical vessels traverse the fetal membranes in the lower uterine segment below the presenting part of the baby. In 6% of singleton pregnancies with a velamentous insertion, vasa previa is a coexisting condition. These unprotected vessels may rupture at any time during pregnancy, causing fetal exsanguination and death. Although spontaneous rupture has been reported before labor and with or without intact membranes, this accident occurs most often during amniotomy. (Quintero, Sepulveda, Romero, et. al.) 
This same placenta is a circumvallate placenta in which the amniotic membranes double back for a short distance over the fetal surface. This decreases the surface area of the placenta reducing delivery of oxygen and nutrients which may lead to fetal growth retardation and/or fetal loss.
In this birth, we were not aware of the placental conditions until after the baby and placenta were born. The birth proceeded smoothly and baby was born gently, without drugs of any kind and no forceful pushing during the second stage of labor. The bag of waters ruptured spontaneously a few minutes before the head emerged. There was no blood in the amniotic fluid and the velamentous vessels were intact upon postpartum examination. The baby was born with high apgar scores, vigorously nursed immediately after birth and has since grown into a vibrant toddler.
This birth accentuates the need for natural childbirth with a watchful birth attendant. This labor was longer than the mother's previous births which would tempt some birth attendants to artificially break the bag of waters. Had we done so, we would have seriously risked rupturing the velamentous vessels and losing the baby.
But if we hope for that we see not, then do we with patience wait for it. Romans 8:25