Refreshing WebI data provider with optional prompt

I am having an issue refreshing a data provider (or document, we've run into the same issue there) which contains an optional prompt.

I'm using a JSON GET to retrieve the parameter values :

{

"parameters" : {

"parameter" : [ {

"id" : 0,

"technicalName" : "psMandatory Prompt 1",

"name" : "Mandatory Prompt 1 :",

"answer" : {

"values" : {

"value" : [ "VALUE1" ]

}

}

}, {

"id" : 1,

"technicalName" : "psMandatory Prompt 2",

"name" : "Mandatory Prompt 1 :",

"answer" : {

"values" : {

"value" : [ "VALUE2" ]

}

}

}, {

"id" : 2,

"technicalName" : "psOptional Prompt",

"name" : "Optional Prompt :",

"answer" : {

"values" : {

"value" : ""

}

}

} ]

}

}

I fill out the values, except for the last one which is not needed, and POST back the JSON.

No matter what I try with the last parameter value, it doesn't seem to "empty" the optional prompt. I've tried removing the parameter from the list, which generates an error; I've tried setting "value" to an empty string or null, which just returns empty results, indicating that the prompt has not been removed from the query.

How do I need to modify this JSON to make my optional prompt disappear?

I'm running 4.2 SP2 patch 2.