This technique was already dismissed by the OP when they wrote, "I can convert the handles from their anchors, but it destroys the shape of curve 1 and 2." The idea is to leave the rest of the path intact.Beginning and end point of a straight line anchor point has to be cropped using alt option. Then you can draw a straight line by pressing shift key. Otherwise you can use convert point tool (last tool in pen tool options) to change the path.
I suppose it was too much to hope that Adobe would make the pen tool function alike in the two programs. That is why I avoid it whenever possible in Ps. It's easier to do it in Ai and just drag it over as a smart object.@agentmoeller
Unfortunately that doesn't work in CS5...nor 2014 for that matter.
The anchor points need to be reset without changing the remaining handles after deleting the offending segment.
I demonstrate this in my video above.
Its a real shame it doesn't work as your method would be the easiest but Adobe never make anything easy....not in PS anyway.....Murphy will get you every time!
As the handle is moved away from the point, it increases the curve. Let's see if I can explain.@IamSam: Interesting, even in my case where the anchor points are not in a non 45 degree increment line, as long as the handles are close to the line's intended vector the result will be 'close enough that no one can tell the difference' (correct?). Do the handles need to be so close to the anchors (could you drag them farther out just to be easier to see / work with? Either way, thank you for the idea, seems really useful.