How to delete empty subfolders with PowerShell?

I have a share that is a "junk drawer" for end-users. They are able to create folders and subfolders as they see fit. I need to implement a script to delete files created more than 31 days old.

I have that started with Powershell. I need to follow up the file deletion script by deleting subfolders that are now empty. Because of the nesting of subfolders, I need to avoid deleting a subfolder that is empty of files, but has a subfolder below it that contains a file.

For example:

• FILE3a is 10 days old. FILE3 is 45 days old.
• I want to clean up the structure removing files older than 30 days, and delete empty subfolders.

C:\Junk\subfolder1a\subfolder2a\FILE3a

C:\Junk\subfolder1a\subfolder2a\subfolder3a

C:\Junk\subfolder1a\subfolder2B\FILE3b

Desired result:

• Delete: FILE3b, subfolder2B & subfolder3a.
• Leave: subfolder1a, subfolder2a, and FILE3a.

I can recursively clean up the files. How do I clean up the subfolders without deleting subfolder1a? (The "Junk" folder will always remain.)