One thing you could try is upping the smoke’s resolution devisions, baking will take longer, but it could give better results. Also, when you up the divisions, you’ll want more particles to fill the same amount of space, so, if you go from 32 to 64, i’d at least double the number of particles.
Also, I can see that you had a couple of strands of smoke escaping from Suzanne. Maybe the resolution of her mesh isn’t high enough? Could try adding a subsurf modifier and applying it, or go into edit mode and subdivide a couple of times, depends on if you want your higher resolution Suzanne to be blocky or smooth (might make a difference with the higher divisions of smoke).
Another thing you could try, not sure if this will work as I haven’t tried it, but you could flip the normals of Suzanne so they’re pointing inwards and use her as the smoke flow object. Get rid of gravity and make sure the smoke sim isn’t using the particles starting speed. This should make the smoke generate at the edges of the mesh and seeing as there aren’t any forces shifting them around, they should stay put.