diff --git a/src/ajax.js b/src/ajax.js
index a6dc4095a..55b528eac 100644
--- a/src/ajax.js
+++ b/src/ajax.js
@@ -746,8 +746,10 @@ jQuery.extend( {
 				response = ajaxHandleResponses( s, jqXHR, responses );
 			}
 
-			// Use a noop converter for missing script
-			if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) {
+			// Use a noop converter for missing script but not if jsonp
+			if ( !isSuccess &&
+				jQuery.inArray( "script", s.dataTypes ) > -1 &&
+				jQuery.inArray( "json", s.dataTypes ) < 0 ) {
 				s.converters[ "text script" ] = function() {};
 			}
 
diff --git a/test/unit/ajax.js b/test/unit/ajax.js
index 125470519..fe831d0b1 100644
--- a/test/unit/ajax.js
+++ b/test/unit/ajax.js
@@ -810,6 +810,19 @@ QUnit.module( "ajax", {
 		};
 	} );
 
+	ajaxTest( "jQuery.ajax() - do execute scripts if JSONP from unsuccessful responses", 1, function( assert ) {
+		var testMsg = "Unsuccessful JSONP requests should have a JSON body";
+		return {
+			dataType: "jsonp",
+			url: url( "mock.php?action=errorWithScript" ),
+			// error is the significant assertion
+			error: function( xhr ) {
+				var expected = { "status": 404, "msg": "Not Found" };
+				assert.deepEqual( xhr.responseJSON, expected, testMsg );
+			}
+		};
+	} );
+
 	ajaxTest( "jQuery.ajax() - do not execute scripts from unsuccessful responses (gh-4250)", 11, function( assert ) {
 		var globalEval = jQuery.globalEval;