Remove empty XML tags

I am looking for a good approach that can remove empty tags from XML efficiently. What do you recommend? Regex? XDocument? XmlTextReader?

For example,

const string original = 
    @"<?xml version=""1.0"" encoding=""utf-16""?>
    <pet>
        <cat>Tom</cat>
        <pig />
        <dog>Puppy</dog>
        <snake></snake>
        <elephant>
            <africanElephant></africanElephant>
            <asianElephant>Biggy</asianElephant>
        </elephant>
        <tiger>
            <tigerWoods></tigerWoods>       
            <americanTiger></americanTiger>
        </tiger>
    </pet>";

Could become:

const string expected = 
    @"<?xml version=""1.0"" encoding=""utf-16""?>
        <pet>
        <cat>Tom</cat>
        <dog>Puppy</dog>        
        <elephant>                                              
            <asianElephant>Biggy</asianElephant>
        </elephant>                                 
    </pet>";