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Is it possible to use JS3Upload with a custom button to select files.
I do not want to use any menu and sub-menus and let users directly click on "Select file to Upload" button.

Also, is it possible to set bucket name and policy/signature programmatically? I'm using JS3Upload with amazon DevPay and asp.net and my users would be redirected to upload page after they select a folder name.
Each user has a unique bucket saved in DB. Policy and signature are being created programmatically within c# code.

Appreciate any help on this.

Yes, it's possible. See i18n_bar_s3.properties and uncomment the following line:
#progress.button.select=Select file(s)

Yes, you can generate signature/policy dynamically on server-side. For DevPay, contact support(at)jfileupload(dot)com to get JFileUpload 2.9 RC which support DevPay.