Change Namespace of element and children

Hi All, new to the list but not new to XSLT.
 
I want to change the namespace of an element using XSLT. My problem is,
I can change the namepsace of a single element easily by doing a
template match and then simply re-adding the element and specifying the
new namespace ... like so:
 
   <xsl:template match="MyElement">
      <xsl:element name="MyElement" namespace="http://www.mystuff.com";>
         <xsl:apply-templates select="@*|*|text()"/>
      </xsl:element>
   </xsl:template>

But, the problem is, child elements of MyElement end up with the default
(empty) namespace ... like so:
 
<MyElement xmlns=http://www.mystuff.com";>
    <MySubElement1 xmlns="">12345</MySubElement1>
    <MySubElement2 xmlns="">12345</MySubElement2>
</MyELement>
 
 
Any ideas? 
 
Thanks,
 
- Kevin

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