EMDR isn't always moving traumatic material material, especially in the beginning. I have to disagree with many of those on here saying not to. When I'm needing stabilization, which I rarely seem to anymore, we use EMDR to strengthen my feelings of trust in myself, awareness of my rights and boundaries, and associations to the present proving I am here and safe.
It also helps me settle down the flooding. My therapist taught me that building resources still improvement. If I don't feel up to moving traumatic material, I ask for resource building only.
EMDR during a second session can be very helpful. I went after a core negative Belief that I held which has made the impact of my traumas worse. I kept telling myself that nobody cares about me. We did some bilateral work and I was able to release a load of anguish and grief as I traveled through my life to all the times I really didn't seem to have anyone who cared. My adult brain was able to recognize that this was playing out in my current life by re-living and re-experiencing that even for things which are relatively no big deal.
It brought me a profound peace.
We get to decide what we want to work on. Go with your gut.