Why won’t certain CSS background-image display in DreamWeaver design mode?

They are correctly showing up in preview and live, but in design view, most of them do show, but I’ve got some that won’t show.
Please note yahooanswers is removing some code and adding "…" but I’m quite sure the code is correct and that it’s a DW issue.

Here is the CSS for one of them:

.tableftside{
background: url(/assets/images/shell/collegeheader_L_corner_gradient.jpg) left top no-repeat;
padding: 4px 8px 4px 24px;
border-right: 1px solid #C1CDE8;
}

(I also tried:
.tableftside{
background-image: url(/assets/images/shell/collegeheader_L_corner_gradient.jpg);
background-repeat: no-repeat;
background-position: left top;
padding: 4px 8px 4px 24px;
border-right: 1px solid #C1CDE8;
}
)

Here is where it shows in the HTML, within several DIV’s:
<ul class="horizontallist">
<li><a class="tableftside home" href="/index.shtml" accesskey="1">College Home</a></li>

Since you seem to be applying this style to a link, try defining your classname as

a.tableftside

and see if that helps.