> Is there a way to pass the parameter if the tested attribute 
> exists and not pass anything, not even an empty string, if it 
> does not?

No: the only way to get the default value is to omit the xsl:with-param
entirely.

It seems you need a different mechanism here, instead of

<xsl:param name="p" select="default"/>

you want

<xsl:param name="p" select="()"/>
<xsl:variable name="p1" select="if ($p) then $p else default"/>

That's 2.0 syntax of course but the principle is the same.

Michael Kay
http://www.saxonica.com/