Boffin1:
So running the LED for half the time only loses a quarter of the perceived brightness, and you could go down to 1:7 ratio before losing half the perceived brightness.

That makes sense, your eyes perceive light intensity as a logarithmic function. Here's the short table I use:

Step | Duty

0 | 0
1 | 1
2 | 3
3 | 7
4 | 15
5 | 31
6 | 63
7 | 127
8 | 255