In short your headphones have too low of an impedance for your phone's amplifier. See below for more details.

How well a system can drive a headphone often stems from two things.

1.) Sensitivity in dB

2.) Impedance

For the Image S3 the specs are:

Sensitivity: 106dB

Impedance: 18 Ohms

http://www.klipsch.com/image-s3-graphite-gray-in-ear-headphones#second

As a general rule of thumb the higher the sensitivity the better easier it is to deliver higher volumes through the headphones. Think of it as efficiency. The higher the efficiency the easier it is to drive the headphones to a louder level.

For impedance, which is certainly trickier, there are two rules of thumb. The first is to avoid headphones and in particular earphones that have an impedance below 20 Ohms. Some systems and thus amps cannot drive low impedance headphones.

Physics

Ohm's Law: V = I*R

Voltage is equal to current in amps ( I ) times the resistance ( Ohms ).

Joule's Law: P = I^2*R or P = V^2/R

Power in watts is equal to the current squared times the resistance or power is equal to the voltage squared over the resistance.

With most amps the voltage is the constant. Once you set it to a level the voltage is fixed. The resistance is the impedance of the headphones which is also fixed ( in most cases ). This leaves the current ( I ) to vary. Keeping this in mind look at the power equation P = V^2/R. The power draw / needed to drive the headphone goes up as the resistance goes down. So the lower the impedance of the headphones the harder is on the amp. The amp or amp section of your phone for example is limited on how much current it can deliver accurately. Similarly working with Ohm's law one can see that V/R = I. Remembering that the voltage is fixed when the volume knob is set we see that as resistance goes down the current goes up.

Unfortunately low impedance headphones can be tricky to drive properly. I have ran into limits like this with the Musichall 25.1 amplifier / DAC. Of course the folks at music hall can give you the schematic for the circuitry so you can modify the output impedance yourself which would prevent this problem in the future.

In your case you may be able to is a Line Out Device ( LOD ) to bypass the phones amp section which may avoid impedance issues.