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Copy contents including the directory itself.
<copy todir="${dest.dir}" >
<fileset dir="${src.dir.parent}">
<include name="${src.dir}/**"/>
</fileset>
</copy>
Note: ${src.dir} is relative to ${src.dir.parent}, and not a full path
You should only have to specify the directory (sans the includes property):
<copy todir="../new/dir">
<fileset dir="src_dir"/>
</copy>
See the manual for more details and examples.