Passage
To him that excelleth. A Psalme of David, when the Prophet Nathan came unto him, after he had gone in to Bath-sheba. Have mercie vpon me, O God, according to thy louing kindnes: according to the multitude of thy compassions put away mine iniquities.
Nearby Context
Psalms 51:1 To him that excelleth. A Psalme of David, when the Prophet Nathan came unto him, after he had gone in to Bath-sheba. Have mercie vpon me, O God, according to thy louing kindnes: according to the multitude of thy compassions put away mine iniquities.
Psalms 51:2 Wash me throughly from mine iniquitie, and clense me from my sinne.
Psalms 51:3 For I know mine iniquities, and my sinne is euer before me.
Study Lenses
The verse centers on "iniquities", "excelleth", "psalme", "david", "prophet", "nathan", "came", and "after". It is saying that the verse draws attention to "iniquities" and "excelleth", so its meaning should be read from those terms before moving to application.
The next verse adds "Wash me throughly from mine iniquitie and...", so "iniquities" and "excelleth" should be read forward into that movement. In Psalms context, the local focus is worship, trust, the LORD's kingship, and covenant mercy.
A plain takeaway is to answer the verse's own emphasis on "iniquities" and "excelleth" with trust shaped by these words, not by a vague optimism outside the passage.