WASHINGTON (CNN) - Top Democratic and Republican senators, negotiating proposed reforms of the use of filibusters and other legislative stalling tactics, are close to an agreement on modest changes to curb the practices but not eliminate them altogether, two Senate aides told CNN.

Despite increased public attention to the often-controversial procedures, supporters of reform don't appear to have enough bipartisan support to force sweeping changes, the aides said. Much of the opposition to the changes comes from senior senators who have seen party control of the Senate switch several times and are wary about giving up the considerable rights available to the minority.