A couple of years ago a dear friend gave me the Banner of Truth "Letters of John Newton." I find myself, in reading them, being "pastored" by someone who's been dead for two hundred years. For all of Newton's wonderful hymns and sermons, his letters were also an important part of his work. Here's a deeply thoughtful section on remaining sin in the believer, written after two letters on the subject of the depravity of the heart. See how well Newton knows his own heart, and therefore the hearts of those to whom he ministers. The letter is entitled "Advantages of Remaining Sin." [!]

If the evils we feel [of remaining sin in us] were not capable of being over-ruled for good, He would not permit them to remain in us. This we may infer from His hatred to sin and the love he bears to His people.
As to the remedy, neither our state nor His honour are affected by the workings of indwelling sin, in the hearts of those whom He has taught to wrestle, strive, and mourn, on account of what they feel. Though sin wars, it shall not reign; and though it breaks our peace, it cannot separate from His love. Nor is it inconsistent with His holiness and perfection, to manifest His favour to such poor defiled creatures, or to admit them to communion with Himself; for they are not considered as in themselves, but as one with Jesus, to Whom they have fled for refuge, and by Whom they live a life of faith. They are accepted in the Beloved, they have an Advocate with the Father, Who once made an atonement for their sins, and ever lives to make intercession for their persons. Though they cannot fulfil the law, He has fulfilled it for them; though the obedience of the members is defiled and imperfect, the obedience of the Head is spotless and complete; and though there is much evil in them, there is something good, the fruit of His own gracious Spirit.

None of this is by way excusing the individual believer for the hardness of his own heart toward others, the living "at this poor dying rate," in view of all that is ours in Jesus. But this is a reminder that, as we are saved by grace, so do we live by grace, always aware of our mixed motives, but also delighting that even our impure motives are over-ruled by Him for His glory and that all of our standing comes by what Jesus has lived for us. This is good news and this is freedom. Somewhere about middle age [or earlier if the Spirit chooses] you start to realize that your every good action is mixed with wrong motives and you fight and not always with the best of success. And you also more deeply feel not only the seriousness and pervasiveness of sin, but the sweetness of what it is to be one with Christ and to receive the benefits He deserved but freely gave to us when He took on the full weight of our every sin past, future, and present. This is the comfort [if we haven't distracted our selves or medicated ourselves] that is ours in the Biblical doctrine of justification, being made right with God. No dry doctrine, that. And few can preach it, even in a letter, like Newton could.