Beginning and ending rag rugs

Hello

This is my first post here, but I've enjoyed reading all the others and learned a lot.  

I've been making rag rugs for a while and am never satisfied with the beginning and ending.  The beginning isn't as difficult because you can weave the next rag strip into the tucked in tip pretty well.  But the ending drives me nuts!   Having part of a row with the rag strip makes my hem look wonky.  Any suggestions?  I use 8/4 cotton rug warp doubled for the hem. 

Ive tried tapering the rag strip, but still not happy. 

Connie