A travel trick I have mentioned here before, several times.

Say you have this.

One solution is to electronically increase contrast:

But you can also put a sharp object in front of the hazy background. Like this:

This gives you the effect of 3D “depth” (the “Close-Far” technique), as well as what I would call “excusable haze”. meaning, the haze has an excuse; no-one will blame you for it. In fact it can help make your foreground object look even sharper.

Those images were from April 2008, by the way.