This is most likely a bug in Firefox. You could do a simple trick to solve this problem: (it's not the best solution, I know, but the problem seems to be serious)
markup: a fake border through a 'wrapper' div
<div class="wrapper">
<div class="box">Hello world</div>
</div>
css: padding does the trick
.wrapper {
border-radius: 15px;
background: #333;
padding:3px; /*simulating border*/
}
.box {
border-radius: 15px;
background: #333;
}
http://jsfiddle.net/steweb/peYRf/
OR a more elegant way to solve the problems (without add another div) could be adding a shadow on the box of the same background-color to 'fill' that white horrible stuff i.e.
.box {
border:3px solid #333;
border-radius: 15px;
background: #333;
-moz-box-shadow:0px 0px 1px #333; /* just on ffox */
}
http://jsfiddle.net/steweb/Sy2rr/
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