There is one strategy which may help. It is called the binomial rule. Establish an upper boundary on the bit rate and render it. If it is OK, pick a much lower bit rate as a lower boundary. Something that is reasonable, but perhaps too ambitious. Render it. If it looks OK, use it as a new upper boundary. Then, try an even lower bit rate, and start over. If it is NOT OK, pick a bit rate half way between the upper and lower boundary. If its OK, set it as a new upper boundary and try again. If its not OK, set it as a new lower boundary and try again.
You will zero in on the right bit rate much more quickly than if you try to work it down one step at a time.
It is really much simpler and easier than it sounds. I hope that description is not too confusing.