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I'm using some content type created by CCK and filefield and the public download counter works OK with the files attached by the filefield module.

I need more detail information on your problem to fix it.

1) absolute path of the drupal root directory in the server
2) absolute path of the public download count installed directory
3) absolute path of a file that does not count
4) URL of the file (see the status bar when you move mouse over to the file download link).
5) confirm that the file name extension of the file is included in the valid extensions of the module settings page.

Thanks,