Need help with append() abd selectors

Need help with append() abd selectors

I have set of ListItems on my page, something like this:

<ul>
  <li>Some value</li>
  <li>Some value</li>
  <li>Some value</li>
</ul>

I need to insert another <li> in the list, such that it becomes the second <li> in the list. e.g.

<ul>
  <li>Some value</li>
  <li>I'm a new list item</li> 
  <li>Some value</li>
  <li>Some value</li>
</ul>

I've been trying to use append() to do this, and that works, but it ends the item as the LAST <li>, not the second one. I'm having some trouble figuring out the correct selector, or method of adding it mid-collection.

Thanks