Minecraft wiki entry for Donkey, associated text: A ridden donkey automatically runs up any one block high slope. The donkey and rider can safely fit through a space as low as 2.75 blocks high. Lower clearance risks suffocating the rider if the rider's head enters a non-transparent block. The donkey itself can enter gaps as low as 1.625 blocks high, but may itself take suffocation damage when clearance is less than 1.75 blocks. They cannot fit through a 1-block-wide gap.