Carets at top of dropdowns

Trying to make carets display only on second-level menu items, not also on third-level menu items.

HTML

<script src="http://unitedwaytoronto.com/prototype/js/jquery.smartmenus.js"></script>
<div id="nav" class="row clearfix show-for-large-up">
    <div class="large-12 columns menucontainer" style="padding-left:0;">
        <ul class="main-menu sm sm-simple">
            <li class="menuItem1 first parent selected"><a href="#">About Us</a>

                <ul class="nccUlMenuSub1">
                    <li class="menuItem1 first parent selected"><a href="#">Our commitment</a>

                        <ul class="nccUlMenuSub2">
                            <li class="menuItem1 first"><a href="#">Operating standards</a>

                            </li>
                            <li class="menuItem2 selected last"><a href="#">Policies</a>

                            </li>
                        </ul>
                    </li>
                    <li class="menuItem2 last"><a href="#">Annual Report</a>

                    </li>
                </ul>
            </li>
            <li class="menuItem2 last parent"><a href="#">Giving</a>

                <ul class="nccUlMenuSub1">
                    <li class="menuItem1 first last"><a href="#">What your gift can do</a>

                    </li>
                </ul>
            </li>
        </ul>
    </div>
</div>

<script src="js/jquery.smartmenus.js"></script>
<script>        
 $(function() {
     $('.main-menu').smartmenus();
   });
 </script>

CSS

/* See: http://www.smartmenus.org/docs/*/

/*Core SmartMenu CSS (do not edit this)*/
.sm,.sm ul,.sm li{display:block;list-style:none;padding:0;margin:0;line-height:normal;direction:ltr;}
ul.sm li{position:relative;}
ul.sm a{position:relative;display:block;}
ul.sm a.disabled{cursor:default;}
ul.sm ul{position:absolute;top:-999999px;left:-800px;width:100px;}
ul.sm li{float:left;}
ul.sm-rtl{direction:rtl;}
ul.sm-rtl li{float:right;}
ul.sm ul li,ul.sm-vertical li{float:none;}
ul.sm a{white-space:nowrap;}
ul.sm ul a,ul.sm-vertical a{white-space:normal;}
* html ul.sm-vertical li{float:left;width:100%;}
* html ul.sm-vertical ul li{float:none;width:auto;}
*:first-child+html ul.sm-vertical>li{float:left;width:100%;}
ul.sm ul.sm-nowrap>li>a{white-space:nowrap;}
ul.sm:after{content:"\00a0";display:block;height:0;font:0/0 serif;clear:both;visibility:hidden;overflow:hidden;}
* html ul.sm{height:1px;}
*:first-child+html ul.sm{min-height:1px;}
ul.sm li *,ul.sm li *:before,ul.sm li *:after{-moz-box-sizing:content-box;-webkit-box-sizing:content-box;box-sizing:content-box;}
ul.sm{-webkit-tap-highlight-color:rgba(0,0,0,0);}

/*SmartMenu CSS that you can customize*/

/* Menu box
===================*/
  .sm-simple,
  .sm-simple ul {
    border:0;
    background:#fff;
  }

 .sm-simple > li > ul {
  border:1px solid #a9abac;
  }

  .sm-simple > li > ul > li > ul {
  border:1px solid #a9abac;
  }  

/* Menu items
===================*/
  .sm-simple a {
    padding:0.4rem 0.8rem;
    color:#000;
    font-size:1rem;
    line-height:1.5rem;    
    text-decoration:none;
    /*border-left:1px solid #eee;*/

  }
  .sm-simple > li > a {
    /*border-left:0;*/
}
  .sm-simple a:hover, .sm-simple a:focus, .sm-simple a:active,
  .sm-simple a.highlighted {
    background:#eee;
    color:#000;
  }
  .sm-simple a.has-submenu {
    padding-right:2rem;
  }
  .sm-simple ul a.has-submenu {
    padding-right:1rem;
  }
  .sm-simple > li > a {
    text-transform: uppercase;
  }
  
/* Sub menu...