What would a negotiated Texas Settlement look like?

The US annexed Texas in 1846, and Polk started a war soon after.

Had the US negotiated the territorial dispute of where the boundary between the US and Mexico would be, what would such a settlement have looked like?
 
This would be after the annexation of Texas, correct?

Mexico could be paid to drop its claims north of the Nueces and the Texan border would be set at the Nueces River, not the Rio Grande. Anything besides that will cause problems. And problems lead to wars.
 
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