Firefox not respecting visibility:hidden on table header - html

Question

I want the header of the first column in my table to be hidden, to get this look:
So I am using the CSS visibility: hidden; to do so. The screenshot above is taken in Chrome, where it works perfectly. However, this happens in Firefox:
How can I make Firefox hide the header of the first column in a table?
EDIT: Here's my table CSS, as requested:
.styledtable{
width:100%;
table-layout:fixed; /*each column same width, unless width explicitly specified*/
border:1px solid black;
border-collapse:collapse;
}
.styledtable td, .styledtable th{
border:1px solid black;
padding:3px;
}
.styledtable th{ background:#cfcfcf; }
.styledtable td{ background:white; }
/* in a table with the first columnn empty (ie. with actions in the column below it),
* make the first column take up space, but not actually appear.
* Usage: <th style="width:40%;" class="firstcol"> </th>
*/
.firstcol{
visibility:hidden;
}
/*every second row different color, if the table itself doesn't have the class "no-odd-row-highlight"*/
.styledtable:not(.no-odd-row-highlight) tr:nth-child(odd) td{ background:#eeeeee; }

Answer 1

This works for me in all major browsers:
<style type="text/css">
table {
border: none;
padding: 0;
border-spacing: 0;
border-collapse: collapse;
}
table th,
table td {
margin: 0;
background: #fff;
border: 1px solid #000;
padding: 0;
}
table th.hidden {
border: none;
visibility: hidden;
}
</style>
<table>
<tr>
<th class="hidden"></th>
<th>ID</th>
<th>Something</th>
</tr>
<tr>
<td>Options</td>
<td>1</td>
<td>---</td>
</tr>
</table>

Answer 2

Depends upon what you want to achieve in styling, but generally, setting relevant element's (color/background-color/border-(top n left)-color(in this case)) to 'transparent' usually works across browsers.
hope this helps someone.