How do I change the spec of a build configuration parameter via the api?

So I have a parameter in my build configuration that is inherited from a template. It is called target_branch.
I can see a listing of it by using: GET http:/myteamcityurl/httpAuth/app/rest/buildTypes/id:buildconfig_QaDeploy/parameters/env.target_branch

which gives me the following data:

<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
<property name="env.target_branch" value="" own="true">
    <type rawValue="select data_2='b' data_1='a' display='normal' data_4='d' data_3='c'"/>
</property>

If I change it to a PUT and add something it goes into the empty value bracket. I need to be able to change the options in the select drop down box and add branches 'e', 'f' and 'g'. I am ok with having to delete the param first and re-creating it as long as I can do it through the API.

Can anyone tell me how to do this?