update query taking too much eventhough used with exists, can we optimize this

UPDATE Elig SET EndDate =
(SELECT MAX(CONVERT(char(8),Row_End_Dt,112))
FROM Enrollment
WHERE ID = Mbr_ID AND CovType = 'DD'
AND EffDate BETWEEN Row_Eff_Dt AND Row_End_Dt
AND EndDate > Row_End_Dt)
WHERE EXISTS (SELECT 'X' FROM Enrollment
WHERE ID = Mbr_ID AND CovType = 'DD'
AND EffDate BETWEEN Row_Eff_Dt AND Row_End_Dt
AND EndDate > Row_End_Dt)