Elle, this is how I do it:
1. Trace an outline of the design onto dull side of freezer paper.
2. Cut out on the line (no seam allowances)
3. Lightly iron to the RIGHT side of fabric. (not alot, just a little to hold it.)
4. Cut out 1/4" away from the edge of freezer paper. (seam allowance)
5. Peel it off, now flip the fabric shape over.
6. Now place the freezer paper sticky side UP on reverse and pin in place.
7. Using a mini clover iron if you have one or the tip of iron turn the edge
over and stick to the freezer paper, snipping into curves to allow fabric
to smooth around easily. Go right around the edge in this way. It's
best if you do this on a hard surface, I used a glass cutting board, you
get a better fix and can mash down any tucks by adding lots of
pressure.
8. When you are happy with it, if you find a little point just peel it off
carefully and iron it on again. Flip it over and IRON it onto your
background fabric. I pinned it as well to be sure it didn't move.
9. Using a small straight stitch, machine all the way around as close as
possible to the edge, I use my open toe foot and reduce foot pressure.
10. Turn over to back side and trim away your background fabric leaving
a 1/4" seam allowance. Now ease the freezer paper out, using your
fingernail on the stitch line and pull horizontally away, it should come
come out quite easily.
Tah dah!!
No more bulk :D
You can do this to 'build' up your applique, so remember to work from the background, underneath areas first. Any areas of overlap don't need to be stitched so just mark lightly where to stitch to and from.
I will still use steam a seam for small pieces, its just too fiddly and time consuming for anything less than a couple of inches or so.
Give it a go and see how you find it :D