Third-party payment processor recommendation - Help Needed!

This question was sent in by an AIMS member who is looking for help with finding a third-party payment processor.

"We are looking for a payment processor, and I don't like the options I have seen thus far:  either they have been too bureaucratic (affiliated entitry of big banks requiring a personal guarantee), or too unreliable and possibly shady (one we have been dealing with in the US), or they don't allow customized branding (PayPal).  We need to be able to accept payments from Visa, Mastercard, Amex and Discover, with the majority of our business coming from corporate users in the US, followed by Europe and Canada, and then the rest of the world.

Do you have any suggestions on reliable but fast-moving companies that provide this service?"