My best advice is try and design your part not to need them. e.g. Chamfer inside corners of overhangs so instead of instead of a T shape you get something like a Y.
I’ve been pleasantly surprised by the amount of times I’ve been able to substantially reduce or even eliminate supports by staying mindful of the constraints of the print process during the design stage.
Of course that isn’t always possible. In that case, as the others said, part orientation and touchpoint size are the knobs you can play with. Discovering how small/sparse you can get away with while maintaining desired tolerances will help.
For a small, very delicate print recently I actually got down to 0.1mm auto-generated touchpoints and then manually placed several ~0.3mm ones where needed (particularly on slicer “islands” where a section of the model begins). I also used third-party software to create a highly-customized structure for tricky areas where Preform would have placed internal supports. You certainly won’t be able to be that aggressive for all types of shapes.
You can also consider breaking apart your model into more than one piece to allow more favorable orientation for problematic sections and gluing them together afterward.