The effects of the new credit card law are beginning to spill over from the issuers to payments networks like Visa Inc. and MasterCard Inc.

In the latest example of an issuer cutting rewards in order to conserve profits, Citigroup Inc. is slashing some travel insurance benefits on its high-end credit cards. But while rewards programs are usually the province of card issuers, these insurance perks are required by the networks, to help distinguish their elite products.

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