General :: Launch Multiple Screen Sessions From A Single Bash Script?

I've written a script (that doesn't work) that looks something like this:

#!/bin/sh
screen -dmS "somename" somecommand
for i in {0..5}; do
screen -dmS "name$i" anothercommand $i
done

For some reason, if I copy and paste this into a terminal, it creates 7 detached screen sessions as I expect. If I run it from within a script, however, I get only the first session, "somename," when I run screen -ls.

Edit: If the same can be accomplished another way (e.g. with multiple screen windows instead of sessions), I would be open those solutions as well.