How can I get a Spring @RestController to accept parameters in JSON format rather than www-form-urlencoded?

Using Spring 4.1.7 on JDK 1.8, I have an @RestController class that looks like this:

@RestController
public class ServiceAController {

    public static final Logger LOG = Logger.getLogger(ServiceAController.class);

    @RequestMapping(value="/rest/servicea", method=RequestMethod.POST)
    public ServiceAResponse serviceA(@RequestParam(value="parmA", defaultValue="defaultParmA") String parmA,
            @RequestParam(value="parmB", defaultValue="defaultParmB") String parmB,
            @RequestParam(value="parmC", defaultValue="defaulParmC") String parmC) {
        LOG.info("Inside Service A handler: " + parmA + " B: "+ parmB + " C: "+ parmC);
}

When I send a POST to /rest/servicea from a javascript like this, everything works, and I see the values "a", "b", and "c" printed in my log:

    var data = {        
        "parmA": "a",
        "parmB": "b",
        "parmC": "c"
    }

    $.ajax({
        type: "POST",
        url: "./rest/servicea",
        contentType: "application/x-www-form-urlencoded",
        data: data,
        dataType: "json",
        success: submitAuthSuccess,
        error: submitAuthFailure 
    })

However, when I try to change the call from the javascript to this (to change the protocol to REST rather than www-urlencode), I get the default values (defaultParmA, defaultParmB, defaultParmC) in my log:

    var data = {        
        "parmA": "a",
        "parmB": "b",
        "parmC": "c"
    }

    $.ajax({
        type: "POST",
        url: "./rest/servicea",
        contentType: "application/json",
        data: JSON.stringify(data),
        dataType: "json",
        success: submitAuthSuccess,
        error: submitAuthFailure 
    })

I think I'm missing something in the @RestController class to get it to parse the JSON rather than expecting www-urlencoded data.

What can I change to make this work, using JSON rather than urlencoded data in the POST body?