In my case, I paid with Google Checkout. It should be more a responsibility for the payment engine (like Google Checkout) to do the fraud detection, not DH’s.
As I observed, Google Checkout is not doing the job very well. For my VISA, there should be a security password requests me to approve the online payment on my side, but Google Checkout did not prompt me for that.
A suggestion from me:
Just open the account immediately after the payment was made through a reliable payment engine (like PayPal?).
If there is any fraud detected later (may be 1 or 2 days later), just close the account immediately. I believe fraud of this kind is not common, because the one who does this has not much to gain.