When we first got our Bluefaced Leicesters (BFL) my first goal was to establish different bloodlines, since they were so rare in the US. Now, 14 years later, there are quite a few breeders, and enough new genetics have been imported from the UK that inbreeding is no longer an issue.
So now - I am selecting for productivity traits. I have a flock that can lamb unassisted, and have nicely shaped udders and well placed teats so that I don't have to supplimental feed the lambs, or help them learn to nurse.
I want ewes with nice, long, strong backs that can carry triplets without becoming broken down and sway-backed. I also select for stock that is up on their pasterns, since my flock is expected to graze year-round. Also, I want heavily pregnant ewes that don't have weak pasterns, and rams that can support their weight on their back legs for breeding.
Like most Leicesters, due to their roman noses BFLs can have bad bites. So I am careful to select for lower teeth that meet the upper dental pad. I also have to watch for good fleece coverage, since BFL are prone to "peeling" along the belly, chest, and around the leg and tail area.
Of course, since I am raising registered stock, I also need to select for proper breed type. Besides good general conformation, I also want good blue skin color, good lock structure in the fleece, a big roman nose, and ears that are properly set.
Its fun, but hard work, and maybe someday I will have "perfect" sheep