You need to find a processor that accepts what is called level 3 payments. This is becoming more and more popular as a form of payment. At our company we do alot of government work and accept this form of payment. I have a couple of companies in california that I represent that do as well. They are actually the least expensive processing rate, but require more detail when entering and not all providers and machines accept them.
Here is a breakdown of all three levels
Level I processing
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Purchases made with personal credit cards issued from U.S. banks qualify as Level I transactions. This means that the only information the merchant must pass to process the transaction is the merchant's name, transaction amount, and the date.
Level II processing
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Level II transactions normally involve corporate cards issued from a U.S. bank. Transactions that qualify for Level II processing cost the merchant less than Level 1 transactions. To qualify for Level II, a transaction must be passed with: merchant name, transaction amount, date, tax amount, customer code, merchant postal code, tax identification, merchant minority code, and merchant state code.
Level III processing
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Of the 3 different levels of credit card processing, Level III provides the lowest transaction processing rate. But, in order to qualify for the lowest rate, Level III transactions must be passed through the processing system with much more detailed transaction information that Level I or II transactions. Because so much information must be transmitted, not all terminals are equipped to process Level III transactions. Purchases that qualify as Level III transactions generally are made with government credit card or corporate cards.