Transparent Transition From Asmx Webservice To Wcf Service

I'm working on a project where I'm replacing an asmx webservice with a wcf service. However, during a transition period, I'd like to have both work for our customers. So I've achieved this somewhat, however I've run into a wall during some testing. I'm getting the following message:

Test method IntegrationTests.StrictMatchTests.StrictProviderPass threw exception: System.Web.Services.Protocols.SoapHeaderException: The message with Action [URL] cannot be processed at the receiver, due to a ContractFilter mismatch at the EndpointDispatcher. This may be because of either a contract mismatch (mismatched Actions between sender and receiver) or a binding/security mismatch between the sender and the receiver. Check that sender and receiver have the same contract and the same binding (including security requirements, e.g. Message, Transport, None)..

I have an asmx file exposed, and I can consume it as a traditional web service. However, they don't seem to be compatible with the older service. If I consume the new service, it works just fine. But I would like this initial transition to be transparent to the end user, and gradually have them consume the wcf service over time.