After incorporating an additional div into Eamon Nerbonne's existing solution, I arrived at the following approach:
Updated jsFiddle
In essence, by introducing another parent div to manage the layout of the subordinate div, you might find success.
<div class="first">
<div class="second">
<table>
<tr><td class="headcol">1</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
<tr><td class="headcol">2</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
<tr><td class="headcol">3</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
<tr><td class="headcol">4</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
<tr><td class="headcol">5</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
<tr><td class="headcol">6</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
<tr><td class="headcol">7</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
<tr><td class="headcol">8</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
<tr><td class="headcol">9</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td><td class="long">QWERTYUIOPASDFGHJKLZXCVBNM</td></tr>
</table>
</div>
</div>
I applied styling to the outer div as shown below:
div.first {
width: auto;
overflow-y: scroll;
overflow-x: hidden;
height: 150px; /* adjust this value based on your requirements */
padding-bottom: 1px;
position: absolute;
left:0;
top:auto;
}