People want SOAP or a WDSL. I've just got a defined API. What's wrong with that?
People are lazy and/or ignorant.
"Web service" is not synonymous with SOAP and WSDL. It's not the only way to do it.
The interesting experiment to run would be to provide a SOAP and WSDL based version of your REST API. Instrument it to see how much each one is used.
I'll bet that, over time, the REST API will get more users due to its simplicity. As long as both are publicized and documented equally well the simpler one will win.
When they say they want SOAP, do they mention WHICH SOAP features they're really after? When I'm doing Java web services, and .Net clients, I personally prefer SOAP so that VS can generate a bunch of .NET classes that'll automagically handle all the network stuff, XML parsing, and object mapping, which while isn't hard, is a PITA. That addresses the lazy issues. If there are OTHER reasons, being able to fall back to an SMTP or other transport layer, which yes, I have actually done with SOAP. Do they have an older service bus that doesn't support REST? Is your interface actually REST? (ok, I said that earlier ). There are a lot of things in SOAP that are addressed in REST with the old YAGNI argument, which is usually true, but not always.