Jamieson, Fausset and Brown on Hebrews 8:6

6. now--not time; but "as it is."

more excellent ministry--than any earthly ministry.

by how much--in proportion as.

mediator--coming between us and God, to carry into effect God's covenant with us. "The messenger (angel) of the covenant."

which--Greek, "one which" [Alford]: inasmuch as being one which.

established--Greek, "enacted as a law." So Ro 3:27, "law of faith"; and Ro 8:2; 9:31, apply "law" to the Gospel covenant. It is implied hereby, the Gospel is founded on the law, in the spirit and essence of the latter.

upon--resting upon.

better promises--enumerated He 8:10, 11. The Old Testament promises were mainly of earthly, the New Testament promises, of heavenly blessings: the exact fulfilment of the earthly promises was a pledge of the fulfilment of the heavenly. "Like a physician who prescribes a certain diet to a patient, and then when the patient is beginning to recover, changes the diet, permitting what he had before forbidden; or as a teacher gives his pupil an elementary lesson at first; preparatory to leading him to a higher stage": so Rabbi Albo in his Ikkarim. Compare Jr 7:21, 22, which shows that God's original design in the old covenant ritual system was, that it should be pedagogical, as a schoolmaster leading and preparing men for Christ.