Extra service shall not be allowed without specific advance approval of the Director of the Budget. Rates of pay for extra service performed by employees eligible to earn overtime in their regular positions shall be determined in the same manner as for overtime (see rules for payment of overtime compensation, section 135.8 of Part 135 of this Title) except that a straight hourly rate shall be paid for those hours worked by an employee as extra service which do not bring the total hours worked by the employee in any one workweek above 40 hours. Extra service performed by an employee not eligible to earn overtime in his regular position shall be compensable at a rate approved by the Director of the Budget.