You can't have a "fixed variable" timestep. It's one or the other.
Of course we need code snippets. We can't read your mind.
My mistake. That was a stupid miswording. It's a fixed timestep (I'll fix that in the question).
There's a lot of different code snippets, so I figured we should start with speculation and theory and then I can get you any specific sections of code you need (i.e. rendering logic, timestep loop, etc.)
How much does it jump/stutter? Could be a rounding error (or lack thereof) when drawing or faulty interpolation.
That or it could just be Swing, if you're using that.
I'm using Math.round when applying the interpolation to rendering positions. That should work fine right?
I am using Swing. The goal of the engine was to use pure Java2D. Surely it can work....