I am looking for a credit card processor for a non-US company, in US$,
for mail-order/telephone-order (not web-placed orders), with a rate
below 5% and not PayPal.

The transaction would be for consultation services.

Three quick questions (and some answers)...
1) is it on the restricted business lists with the primary acquirering
banks (merhant processing banks)?  If yes - you won't get it on-shore.
2) do you have a US based bank account for funding? If no - again, forget it.
3) what kind of volume and ticket sizes are you talking about (the
higher the volume - the riskier the business - the higher the required
reserves or hold-backs).