The key issue for a merchant is to offer the potential buyers a payment tool they are familiar with and they have in their pocket (or virtual pocket). Credit cards, despite their liability disadvantages, have these characteristics.

Merchant fraud costs:
Average fraud costs are reported to be lower than 1-3% (CNN.com, although for high risk goods, cross-border purchases and when no risk management tools are in place, fraud size can go over 20% (BuyDirect Inc).

Merchant Anti-fraud measures:
The role of merchants in fraud prevention by screening fraudulent
transactions is often overlooked.

The lack of consumer authentication by issuer banks combined
with merchants' liability for fraudulent credit card transactions have
motivated the development of merchant-_base_d authentication solutions,
reducing on-line fraud by 66-80%.

These solutions include:
- address validation,
- on-line authorisation,
- customer follow-up (e-mail confirmation, etc),
- customer history data_base_ consultation,
- fraud scoring systems,
- customer data format and content editing rejecting orders with incomplete information,
- proof of delivery to the verified billing address,
- domain site check,
- application of additional measures for high risk purchases (call customer, ask for issuer bank and phone number, exact name on credit card),
- state in web site that anti-fraud measures have been put in place , etc.

I hope it helps and would welcome any comment.