@EJB injection fails in @Named bean when interceptor is present

I have a @Named bean in which I'd like to inject a component, using @Inject as well as a stateless session bean, using @EJB. The ejb is accessed using the no-interface view. Both references get injected properly in that case, but when I use an interceptor on one of the methods, only the references annotated with @Inject get injected, whereas those annotated with @EJB don't.

The interceptor doesn't need to do anything special, this behaviour occurs even if only proceed() is invoked on the invocation context - the interceptor is always invoked correctly.

The following snippet explains the issue:

@Named
public class MyController {

@EJB
private MyDao dao;

@Interceptors(MyInterceptor.class)
public void control()

}

---------------------------------------------------------------
@Stateless
public class MyDao {

public void doDataAccessStuff()

}
---------------------------------------------------------------
public class MyInterceptor {

@AroundInvoke
public Object intercept(InvocationContext context) throws Exception

}