ng-maxlength screws up my model

When your textarea exceeds 15 characters, result becomes undefined — that’s just how the ng-min/maxlength directives work. I think you’ll have to write your own directive. Here is a directive that will block input after 15 characters:

<textarea my-maxlength="15" ng-model="result"></textarea>

app.directive('myMaxlength', function() {
  return {
    require: 'ngModel',
    link: function (scope, element, attrs, ngModelCtrl) {
      var maxlength = Number(attrs.myMaxlength);
      function fromUser(text) {
          if (text.length > maxlength) {
            var transformedInput = text.substring(0, maxlength);
            ngModelCtrl.$setViewValue(transformedInput);
            ngModelCtrl.$render();
            return transformedInput;
          } 
          return text;
      }
      ngModelCtrl.$parsers.push(fromUser);
    }
  }; 
});

fiddle

Update: to allow more than 15 characters, but disable the submit button when the count exceeds 15:

link: function (scope, element, attrs, ngModelCtrl) {
  var maxlength = Number(attrs.myMaxlength);
  function fromUser(text) {
      ngModelCtrl.$setValidity('unique', text.length <= maxlength);
      return text;
  }
  ngModelCtrl.$parsers.push(fromUser);
}

fiddle