This can be done using CSS3 columns quite easily. Here’s an example, HTML:
#limheight {
height: 300px; /*your fixed height*/
-webkit-column-count: 3;
-moz-column-count: 3;
column-count: 3; /*3 in those rules is just placeholder -- can be anything*/
}
#limheight li {
display: inline-block; /*necessary*/
}
<ul id = "limheight">
<li><a href="">Glee is awesome 1</a></li>
<li><a href="">Glee is awesome 2</a></li>
<li><a href="">Glee is awesome 3</a></li>
<li><a href="">Glee is awesome 4</a></li>
<li><a href="">Glee is awesome 5</a></li>
<li><a href="">Glee is awesome 6</a></li>
<li><a href="">Glee is awesome 7</a></li>
<li><a href="">Glee is awesome 8</a></li>
<li><a href="">Glee is awesome 9</a></li>
<li><a href="">Glee is awesome 10</a></li>
<li><a href="">Glee is awesome 11</a></li>
<li><a href="">Glee is awesome 12</a></li>
<li><a href="">Glee is awesome 13</a></li>
<li><a href="">Glee is awesome 14</a></li>
<li><a href="">Glee is awesome 15</a></li>
<li><a href="">Glee is awesome 16</a></li>
<li><a href="">Glee is awesome 17</a></li>
<li><a href="">Glee is awesome 18</a></li>
<li><a href="">Glee is awesome 19</a></li>
<li><a href="">Glee is awesome 20</a></li>
</ul>