Changing an element’s ID with jQuery

I need to change an element’s ID using jQuery.

Apparently these don’t work:

jQuery(this).prev("li").attr("id")="newid"
jQuery(this).prev("li")="newid"

I found out that I can make it happen with the following code:

jQuery(this).prev("li")show(function() {
    this.id="newid";
});

But that doesn’t seem right to me. There must be a better way, no? Also, in case there isn’t, what other method can I use instead of show/hide or other effects? Obviously I don’t want to show/hide or affect the element every time, just to change its ID.

(Yep, I’m a jQuery newbie.)

Edit
I can’t use classes in this case, I must use IDs.