Adjust list style image position?

Not really. Your padding is (probably) being applied to the list item, so will only affect the actual content within the list item.

Using a combination of background and padding styles can create something that looks similar e.g.

li {
  background: url(images/bullet.gif) no-repeat left top; /* <-- change `left` & `top` too for extra control */
  padding: 3px 0px 3px 10px;
  /* reset styles (optional): */
  list-style: none;
  margin: 0;
}

You might be looking to add styling to the parent list container (ul) to position your bulleted list items, this A List Apart article has a good starting reference.

I normally hide the list-style-type and use a background image, which is moveable

li 
{
    background: url(/Images/arrow_icon.gif) no-repeat 7px 7px transparent;
    list-style-type: none;
    margin: 0;
    padding: 0px 0px 1px 24px;
    vertical-align: middle;
}

The "7px 7px" is what aligns the background image inside the element and is also relative to the padding.

A possible solution to this question that wasn't mentioned yet is the following:

    li {
        position: relative;
        list-style-type: none;
    }

    li:before {
        content: "";
        position: absolute;
        top: 8px;
        left: -16px;
        width: 8px;
        height: 8px;
        background-image: url('your-bullet.png');
    }

You can now use the top/left of the li:before to position the new bullet. Note that the width and height of the li:before need to be the same dimensions as the background image you choose. This works in Internet Explorer 8 and up.

I had the same problem, but i could not use the background option (and didn't want to use multiple backgrounds) so i thought of another solution

this is an example for a menu that has a square like indicator for the active/current menu item (the default list style is set to none in another rule)

nav ul li.active>a:before{
    content: "■";
    position: absolute;
    top: -22px;
    left: 55px;
    font-size: 33px;

}

it creates a square by using a square character with the ":before" pseudo class and it is freely positionable by using absolute positioning.