Possible to configure such that users can only delete their own records?

Possible to configure such that users can only delete their own records?

I want to configure the system such that non-Admin users can only delete their own records. Is it possible to do this? I have been fiddling around with Profile settings and Data Sharing settings but the results seem to be inconsistent.

I had:
  1. enabled Delete rights for a module in a Profile (e.g. Accounts).
  2. In Data Sharing settings, I had set Private access for Accounts module and created two new Data Sharing rules:
    1. One rule giving Read/Write access to all users with data shared by all users
    2. Another rule giving Read/Write/Delete access to Admin users with data shared by all users
The result I got was the non-Admin users are still able to delete records in that module... It looks like rule 2a has no effect.