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Thank you for being my follower, I hope that you find my posts useful.

I felt a little concern about putting in my Steemit password into a nonSteemit website? Is anyone feeling the same and what have you found that may put me to ease?

Make sure you put yourself your active key in stead of master key and you will be fine, because with master key you can change all the other keys. And as far as I know steemfollower website does not keep your password on their server, it is only kept in your browser.
I got used to insering passwords after using sites like steemvoter and steemian. Happy Steeming!