Limiting Y Movement (where Y is flexible)

Hi, I want to make a Double Dragon like game. If you remember, that game was a simple 2D scroll but the player had about a 1/3 of the screen to move up and down(y axis) while an essentially limitless X. What I am wondering, since there will be some parts where the players path will narrow and widen, so Y movement amount will change, what is the best way to do this?

Obviously with world limits I would be stuck to a rigid system, not good. The other I think would be to set up walls, objects, through which the player cannot pass, however, in terms of aesthetic, the player's head would bump into the wall, when he should be able to go as hi so his feet match just below the walls foot. So I am currently approaching this programming issue, if anyone has any ideas, suggestions, I would love to hear them. Thanks!