Williams told www.scottishrugby.org: "It's a pretty good draw, particularly given that we won't be facing Argentina, Fiji or Samoa in the pool stages. "We've drawn the All Blacks and, in all probability, Italy, and we know plenty about both of them.
"Qualification for the knockout stages of the World Cup isn't easy and to be honest all four pools are tough." The 2007 tournament is being hosted in France with pool matches scheduled to be staged in Scotland, Wales and Ireland.
Scotland will play three of their four pool games at Murrayfield. The expectation is that the top game in the pool - Scotland v New Zealand - would be one of those games at Murrayfield but the exact split of the fixtures has yet to be determined.