Here's a method I think I might try.
Roll the hit die together with 1d4. Take whichever roll is higher.
With this method, a magic-user has a 1/16 chance of getting a 1, a thief a 1/24 chance, a cleric a 1/32 chance, a fighter a 1/40 chance, and a barbarian a 1/48 chance. So it would tend to...