I like using tiny rolled up Glue Dots instead of mounting tape to secure delicate pieces like branches and foliage. I keep the 1/8”, 3/16” and 3/8” on hand all the time. I pick the dot up off the roll using the pointed tip of my paper piercer and gently roll the ball. I don’t handle it too much as the oil from my fingers can ruin the stickiness. If I need adhesive to pop up a really thin piece like the tips of the branches I roll the dot into a thin line of adhesive. This method works great even with the tiny 1/8” dot.
You can see the dimension this adds while securing the die cut to your project.