webService.SoapVersion =
System.Web.Services.Protocols.SoapProtocolVersion.Soap12;
[Edit 9 Dec 2010]
Actually, this was a red herring. It worked by adding a "service reference", rather than a old-fashioned "web reference".
ASP.NET, Visual Studio, C#, Sitecore Content Management System
webService.SoapVersion =
System.Web.Services.Protocols.SoapProtocolVersion.Soap12;
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