These iPhone 6S measurements might be interesting to some of you. This is for model MKTG2LL/A with iOS version 9.0.2 (13A452).

Open-circuit voltage, right channel, maximum volume
It's exactly 1V, a little lower than the maximum volume of the 5S. The volume control is very coarse: -3 dB and -4 dB steps:
Voltage, mV
| Attenuation from max, dB |
1000 | 0 |
709 | -2.99 |
450 | -6.94 |
320 | -9.90 |
204 | -13.81 |
146 | -16.71 |
91.7 | -20.75 |
58.8 | -24.61 |
38.8 | -28.22 |
24.3 | -32.29 |
16.6 | -35.60 |
10.1 | -39.91 |
7. | -43.10 |
It goes from maximum volume to mute with 16 presses of the volume down button. 8 down has the volume level indicator halfway through the scale, 38.8 mV or roughly 28 dB down.
Here's what happens with 16 ohms across each channel:

Right Channel Voltage, 16-ohm load on right channel only

Right Channel Voltage, 16-ohm load on each channel

Left Channel Voltage, 16-ohm load on each channel
The impulse response and some square waves:

Impulse response

1 kHz square wave

Rising edge of 60 Hz square wave
Here's what happens to at lower voltage levels, which is where you usually have it when listening to earphones:

Right channel, open circuit voltage, 5 clicks down from maximum.

The same, but with a 16-ohm load on each channel
Let Wolfram Alpha do the work:
http://www.wolframalpha.com/input/?i=201*16.2%2F%28R%2B16.2%29+%3D+156
It should be ok with the usual dynamic-driver IEMs, low-impedance dynamic-driver headphones with relatively flat impedance vs. frequency graphs, e.g., ATH-M50x, and BA IEMs that sound better with added serial resistance, e.g., ER4P, UE600 with foam tips, Apple ME186LL/A.
With really sensitive IEMs that have crazy impedance vs. frequency curves, I guess you could build the following circuit to make them work better with the iPhone 6S (or for that matter, those "premium" portable music players that have it much worse).

The iPhone 6S will see a near-constant 16-ohm load, the IEM will see slightly less than 1 ohm source impedance, the frequency response going to the IEM will be much flatter, and the signal-to-noise ratio will be improved.
I'll see if I can take measurements to show what happens to the noise level when scrolling, switching apps, etc.