Automatically convert songs to a lower bitrate makes little difference

I have 8.31GB of music on my computer (all >= 256kbps), but only 6.7GB of free space on my phone. I though, OK if I downconvert to 256kbps it should fit on. Nope, it still takes 7.7GB. I thought okay, logically 192kbps should be 3/4 of that; nope again 7.5GB. Again, 128kbps is too big: 7.36. How come halving the bitrate only makes a tiny difference to the file size? 256kbps for my 3 days and 3 hours of music should take about 8.6GB:

((3*86400 + 3*3600) * 256000)/8000000000

and 128kbps should take up 4.3GB:

((3*86400 + 3*3600) * 128000)/8000000000

So, what is taking up all the extra space and how can I resolve this while keeping all my music on my phone?

iPhone 5S 16GB

iOS 6.3

iTunes 12.1.2.27 on Windows 10 build 1061(But I have had the same problem on Windows 7 - I removed some music because some of it I didn't really want - no longer the case)