Brain Game: Hoof on Roof

By changing one letter at a time to form different English words, and leaving all other letters in their original positions, convert REIN into DEER in the fewest steps possible. Good luck!

R E I N _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ D E E R

Here is a 6-step SOLUTION.

AN 8-STEP SOLUTION:

REIN > VEIN > VEIL > VEAL > DEAL > DEAR > DEER

Did you come up with a different or shorter sequence of words? Feel free to show off your work by commenting below.