Character shadows lost with baked light

I have a human character in the scene. I want to use it with baked light. I set it “static” as well as the floor and the wall.
But when I change the baking of my only directional light source from “realtime” to “baked”, the shadow cast by the character disappears, although the shadow cast by the wall remains as it should.

I want the shadow of the character to be seen properly. What am I doing wrong?

I am using Unity 5.3.

Use realtime.

I would prefer baked light, because it looks much better (and in this project I don’t need to move the characters, they will be like statues, so they can remain static).

Get 5.4 beta and switch to mixed.

Ok, I’ll try that. Thank you!