Managing incomplete application submissions

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Hi all,

For certain of our jobs, we require applicants to submit a number of documents along with their application.  While we lay this out pretty explicitly in the job descriptions, we have found that many of our applicants are submitting their application and did not include all of the attachments that we asked for.  One reason for this is because we have not made uploading attachments required, as some of our positions only require one piece of supporting documentation (such as a cover letter), while others may require as many as 5.

I'm wondering whether other places have had this problem and how you managed it?  Thanks for your feedback!