The contradictions between Luke and Matthew on Jesus birth?

According to Matthew, Jesus was born during the reign of Herod the Great (Matthew 2:1). According to Luke, Jesus was born during the first census in Israel, while Quirinius was governor of Syria (Luke 2:2). This is impossible because Herod died in March of 4 BC and the census took place in 6 and 7 AD, about 10 years after Herod's death. Does any body else find this odd ?