Why does my hover background extend past container - css

Question

I am relatively new to CSS and tried to create a CSS DropDown menu.
After many hours of css reading I have created one, but the last child on the parent UL bleeds over when on hover.
Here is JSFiddle link: JSFiddle Code
<mini-nav>
<ul>
<li>Services
<ul>
<li>Service 1</li>
<li>Service 2</li>
<li>Service 3</li>
<li>Service 4</li>
</ul>
</li>
<li>Security
<ul>
<li>Security 1</li>
<li>Security 2</li>
<li>Security 3</li>
</ul>
</li>
<li>Centres
<ul>
<li>Centres 1</li>
<li>Centres 2</li>
<li>Centres 3</li>
</ul>
</li>
</ul>
mini-nav ul
{
width: 237px;
text-align: center;
display: inline;
margin: 0;
padding: 5px 0 5px 0px;
list-style-type: none;
-moz-border-radius: 5px;
-webkit-border-radius: 5px;
border-radius: 5px;
background: #58585A;
box-shadow: 3px 3px 5px #828282;
}
mini-nav ul li
{
font-size: 13px;
display: inline-block;
margin-right: -4px;
position: relative;
width: 78px;
padding: 5px 0 5px 0px;
border-right: 1px solid white;
cursor: pointer;
-webkit-transition: all 0.2s;
-moz-transition: all 0.2s;
-ms-transition: all 0.2s;
-o-transition: all 0.2s;
transition: all 0.2s;
}
mini-nav ul > li:last-child
{
border-right: none;
}
mini-nav ul li:hover
{
background: #E8E8E8;
color: black;
background-image: url(../mes-images/menu-topper.png);
background-position: top left;
background-repeat: repeat-x;
display: inline-block;
}
mini-nav ul li:hover:first-child
{
-moz-border-radius: 5px 0 0 0;
-webkit-border-radius: 5px 0 0 0;
border-radius: 5px 0 0 0;
-webkit-background-clip: padding-box;
-moz-background-clip: padding;
background-clip: padding-box;
}
mini-nav ul li:hover:last-child
{
-moz-border-radius: 0 5px 0 0;
-webkit-border-radius: 0 5px 0 0;
border-radius: 0 5px 0 0;
-webkit-background-clip: padding-box;
-moz-background-clip: padding;
background-clip: padding-box;
}
mini-nav ul li:hover a
{
color: black;
}
mini-nav ul li:hover ul
{
display: block;
opacity: 0.8;
visibility: visible;
}
mini-nav ul li a
{
color: White; text-decoration: none;
}
mini-nav ul li ul
{
text-align: left;
padding:0;
position: absolute;
top: 27px;
left: 0;
width: auto;
display: none;
visibility: hidden;
-webkit-transiton: opacity 0.2s;
-moz-transition: opacity 0.2s;
-ms-transition: opacity 0.2s;
-o-transition: opacity 0.2s;
-transition: opacity 0.2s;
-moz-border-radius: 0 0 5px 5px;
-webkit-border-radius: 0 0 5px 5px;
border-radius: 0 0 5px 5px;
}
mini-nav ul ul > li:last-child
{
border-bottom: none;
}
mini-nav ul li ul li:hover
{
background: #E8E8E8;
color: black;
width: 110px;
}
mini-nav ul li ul li
{
display: block;
color: #fff;
width: 110px;
border-bottom: solid 1px silver;
padding-left: 12px;
border-right: none;
margin-right: 0;
}
mini-nav ul li ul li:hover:last-child
{
-moz-border-radius: 0 0 5px 5px;
-webkit-border-radius: 0 0 5px 5px;
border-radius: 0 0 5px 5px;
}
I apologize for my bastardized css!!!

Answer 1

On your Css, find this code
mini-nav ul > li:last-child { border-right: none; }
and add "margin:0" into it so it like this :
mini-nav ul > li:last-child { border-right: none; margin:0; }
Finally, this is what you want ?
DEMO
Working code if link was broken :
/* Parent CSS */
mini-nav ul {
width: 237px;
text-align: center;
display: inline;
margin: 0;
padding: 5px 0 5px 0px;
list-style-type: none;
-moz-border-radius: 5px;
-webkit-border-radius: 5px;
border-radius: 5px;
background: #58585A;
box-shadow: 3px 3px 5px #828282;
}
mini-nav ul li {
font-size: 13px;
display: inline-block;
margin-right:-4px;
position: relative;
width: 78px;
padding: 5px 0 5px 0px;
border-right: 1px solid white;
cursor: pointer;
-webkit-transition: all 0.2s;
-moz-transition: all 0.2s;
-ms-transition: all 0.2s;
-o-transition: all 0.2s;
transition: all 0.2s;
}
mini-nav ul > li:last-child { border-right: none; margin:0; }
mini-nav ul li:hover
{
background: #E8E8E8;
color: black;
background-image: url(../mes-images/menu-topper.png);
background-position: top left;
background-repeat: repeat-x;
display: inline-block;
}
mini-nav ul li:hover:first-child {
-moz-border-radius: 5px 0 0 0;
-webkit-border-radius: 5px 0 0 0;
border-radius: 5px 0 0 0;
-webkit-background-clip: padding-box;
-moz-background-clip: padding;
background-clip: padding-box;
}
mini-nav ul li:hover:last-child {
-moz-border-radius: 0 5px 0 0;
-webkit-border-radius: 0 5px 0 0;
border-radius: 0 5px 0 0;
-webkit-background-clip: padding-box;
-moz-background-clip: padding;
background-clip: padding-box;
}
mini-nav ul li:hover a { color: black; }
mini-nav ul li:hover ul {
display: block;
opacity: 0.8;
visibility: visible;
}
mini-nav ul li a { color: White; text-decoration: none; }
/* Child CSS */
mini-nav ul li ul {
text-align: left;
padding:0;
position: absolute;
top: 27px;
left: 0;
width: auto;
display: none;
visibility: hidden;
-webkit-transiton: opacity 0.2s;
-moz-transition: opacity 0.2s;
-ms-transition: opacity 0.2s;
-o-transition: opacity 0.2s;
-transition: opacity 0.2s;
-moz-border-radius: 0 0 5px 5px;
-webkit-border-radius: 0 0 5px 5px;
border-radius: 0 0 5px 5px;
}
mini-nav ul ul > li:last-child { border-bottom: none; }
mini-nav ul li ul li:hover {
background: #E8E8E8;
color: black;
width: 110px;
}
mini-nav ul li ul li {
display: block;
color: #fff;
width: 110px;
border-bottom: solid 1px silver;
padding-left: 12px;
border-right: none;
margin-right: 0;
}
mini-nav ul li ul li:hover:last-child {
-moz-border-radius: 0 0 5px 5px;
-webkit-border-radius: 0 0 5px 5px;
border-radius: 0 0 5px 5px;
}

Answer 2

It's because .mini-nav ul li is
position:relative;
margin-right:-4px;
You've made it go right 4 pixels and that's throwing it out.