JAX-WS - Map Exceptions to faults

I am using JAX WS to expose a WebService. Some of the operations of this service can generate exceptions. Not internal server exceptions, but rather exceptions that are dependent on the input arguments of the operation invocation.

If I specify that my operation throws a custom Exception, like so:

@WebService
@SOAPBinding(style = Style.RPC, use = Use.LITERAL)
public class MyServiceEndpointImpl implements MyServiceEndpoint {

    @WebMethod
    public void throwsException throws InvalidInputException;
}

I end up with the following stacktrace when running the application:

 com.sun.xml.ws.model.RuntimeModelerException: runtime modeler error: Wrapper class com.mypackage.ws.services.jaxws.InvalidInputExceptionBean is not found. Have you run APT to generate them?
    at com.sun.xml.ws.model.RuntimeModeler.getClass(RuntimeModeler.java:285)
    at com.sun.xml.ws.model.RuntimeModeler.processExceptions(RuntimeModeler.java:1006)
    at com.sun.xml.ws.model.RuntimeModeler.processRpcMethod(RuntimeModeler.java:969)
    at com.sun.xml.ws.model.RuntimeModeler.processMethod(RuntimeModeler.java:546)
    at com.sun.xml.ws.model.RuntimeModeler.processClass(RuntimeModeler.java:370)
    at com.sun.xml.ws.model.RuntimeModeler.buildRuntimeModel(RuntimeModeler.java:256)
    at com.sun.xml.ws.server.EndpointFactory.createSEIModel(EndpointFactory.java:322)
    at com.sun.xml.ws.server.EndpointFactory.createEndpoint(EndpointFactory.java:188)
    at com.sun.xml.ws.api.server.WSEndpoint.create(WSEndpoint.java:467)
    at org.jvnet.jax_ws_commons.spring.SpringService.getObject(SpringService.java:333)
    at org.jvnet.jax_ws_commons.spring.SpringService.getObject(SpringService.java:45)
    at org.springframework.beans.factory.support.FactoryBeanRegistrySupport$1.run(FactoryBeanRegistrySupport.java:121)

Adding @XmlRootEntity to InvalidInputException does not solve the problem.

If this is