Allegations of a global scheme to cleanse dirty money in U.S. banks have led to renewed calls for tougher anti-money-laundering rules. But lawmakers will have to walk a fine line between the conflicting goals of security and privacy, and banks may once again be caught in the middle.

Last week, House Banking Chairman Jim Leach proposed legislation that would force U.S. banks to take extra precautions before doing business with foreign customers. The White House shortly thereafter offered a combination of legislative and regulatory fixes.

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