The Law Within the Heart

Sixteen hymns in our new hymnal by Timothy Dudley-Smith, several mentioning God's sovereignty.  Overall there's not really anything wrong with them, but there are so many richer options.  And I tend to get cranky over the line that says Christ's sacrifice for sin begins "the covenant of grace, the law within the heart."  When the line flies past during a church service, it always strikes me as equating grace and law.

Now, if we understand "the law within the heart" not to be a new law, new rules, new demands, maybe this turn-of-phrase could be okay.  Between Hebrews (10 and 8) and Jeremiah (31), the "law within the heart" appears to be freedom from the written code of the law, the mercy of God poured out on you so that you are made new, and so that you joyfully and freely do what is good and right and of service to the neighbor.

Is that what the hymn indicates?  I don't know.  But this is what I'm trying to convince myself it's saying.