I find that when I dissolve edges at the boundaries of an object it tends to delete more than I wanted. See example below.
In this situation, delete edge is even better because at least then the other edges are there and I can rebuild the faces.
Why does this happen? Is it a bug? Because sometimes I do the same procedure on the same geometry and it works as it should and I don’t know why.
You’re trying to leave an L-shaped n-gon that Blender recalculations can’t properly handle.
Why do you need to remove that crucial edge?
Sorry I should have been more specific. I’m working with a triangular shape with subsurf and I keep hearing how triangles are bad, so I’m trying to make it into quads like the below screenshot. But when I delete those edges it removes more geometry than I want.
N-gons are bad if they leave inaccuracies on the finished surfaces when using subsurface modifier. If you’re working with a flat surface, they should be okay.
What you show in that last image should work. That’s how I would do it.
Now all you do is add a loop around the very edge to pull the corners sharp.
EDIT: I just tried it and I see what you mean with the corners. The corner vert is being deleted when you disolve the edge.
You can’t delete/dissolve an edge/edge loop without deleting that point at the end if it does not share geometry with another edge.
In the case of no other geometry select the faces and use “f” for merge faces.
Nice trick! I didn’t know 'f’would do that!
oops sorry. I meant to reply to you. Answer above. 
Using 2.82 here, the “Adjust Last Operation” panel (in edge selection) has an option for that. Also you can use Ctrl x (Dissolve, Context-Sensitive) and limited dissolve with different applications. The Dissolve Verts option is not listed in the manual.
two great tips!
I’m glad its useful.
Perfect that’s just what i needed!
fantabulous
