Help with modelling

Hi folks. I’ve been trying for a while to model this thing, which is some sort of inorganic object. What I got so far is this:

If look closely there is hard edges in parts where I don’t want them to be. I want it to be more like this (which is a poorly made paint over):

I tried everything: extra edge loops, adjusting the crease, edge split, you name it. I always get either the sharps edges or (when I adjust the crease) weird geometry.
Is there a way to accomplish what I want? You can find the .blend file here:

One side of the objects I left with the extra edge loops and the other got none.

What version are you using? Go into edit mode. Select all your vertices. Press Ctrl + E. Click “shade smooth”. Then, still in edit mode, select the edges that you want to be hard edges. Press Ctrl + E again. This time select “mark sharp”. Then go into the modifiers section for the object. Add an edgesplit. Turn on “Sharp edges” in the modifier and then turn off “Edge Angle” in the modifier! There you go! Happy blending.

This is actually a pretty difficult shape to do if you want it to be perfect
You could do it using edge creases (shift+e) or by merging the edges on the sides but not at the top and bottom

Here’s my version (from scratch, not from your .blend): first the overall effect, and then the cage before and after subsurfing.

The convex corners (such as the one circled green in the following image) are no problem: they can be simple cross hatch corners, giving sharp edges without disrupting the overall shape.

The saddle-point corners (circled red) are more awkward. They must be edge-flow corners, so the extra edge loops required to make the sharp edge of the step have to continue on somewhere. Continued along the length of the cylinder, they will produce unwanted creases, as you found. The solution is to continue them instead around the circumference of the cylinder, where extra loops can be introduced with no adverse effects.

Best wishes,

Done the convex corner, and it looks just fine. The other point is taking me a little more effort but I’ll get it right. I’ll try to follow you model more closely.

Thank you very much for you advice.