This applies to FM broadcasting, and the broadcasting of music as opposed to exclusively voice. Types of FM broadcasting include low power FCC Part 15 compliant devices and LPFM (Low Power FM) broadcasting such as college campus radio or community radio. The discussion assumes the use of FCC complaint equipment and operating within the boundary of law for your area. This applies to FM Broadcast Stereo transmission on the 3 Meter FM Broadcast Radio band within the legal limits of power, antenna height, emission regulations, FM Broadcast Radio Frequency Deviation, and other related regulations.
The problem: Your low power FM station is very noticeably quieter than the high power FM broadcast stations you share the spectrum with. When you try to increase the input volume into your transmitter, you either start to produce terrible distortion in the music (poor audio quality), clipping (audio cuts out at peeks), or you exceed the legally allotted bandwidth (deviation) which results in a number of issues including those previously mentioned. Boosting your transmit power is not the solution and may get you into trouble. More transmit power just means more people will hear your distortion as well as other negative consequences.
Turn up the receiver: Some people say, "so what? just turn up the radio receiver!" However this is a very short-sighted and unsatisfactory solution. The first and most obvious problem is that if you encounter any kind of interference (due to tropospheric ducting or otherwise) or you forget your volume is high and tune your receiver to another station then you get an unpleasant blast from the speaker, bad for your hearing and the speakers on the receiver! It would be much better if your transmission was at or at least near the same level of loudness as other stations.
An audio source, such as an iPod, will produce good quality full spectrum sound. What the average Joe doesn't realize that when listening to music from an FM radio broadcast station, they are not getting the same rich full spectrum sound that they get from their iPod. Assuming that the digital source is not manipulated, it will have the very low end of the audio spectrum you can hear as well as the very high end fully intact from what the artist originally created (for the most part without getting to technical).
FM radio broadcasters wanted a way to cheat, and make the music from their radio station stand out more by being louder, but without exceeding legal FM Broadcast Radio Frequency Deviation. To simplify the discussion we can sum up what they did by saying that they cut off the very low and high end of the spectrum, and squeezed it all together just enough to be louder without distorting it noticeably. Less dynamic range means less audio information to transmit on the radio signal, so the spectrum segment allowed can be max out with louder music.
After you have come to terms with the fact that your FM transmission will never be of the same quality, clarity, and full spectrum sound as the source audio, you can now consider means to process the audio you send to your transmitter so that it can be louder without clipping and distorting. Your end goal is to be of comparable quality to other FM radio broadcasts and at near the same level of loudness.
Source to Radio Transmitter:
From a high quality audio source such a computer with high-end sound card, or a quality iPod music player (they're pretty good) your full spectrum sound will be sent to the FM transmitter. Assuming it is a good transmitter (something that's going to cost at least in the 3 digit range) and your radio receiver is of unusually high quality the only way you are going to be able to avoid distortion is to limit the input volume. The spectrum space your transmitter has to work with can only handle so much. The louder the volume, the greater the deviation (how wide the modulation is) and you're either going to have to sacrifice quality or volume. If you hate "compression" then you're out of options.
Some better quality consumer grade FM transmitters include a rather effective Automatic Gain Control (AGC) circuit that can allow you to increase the input volume without as much distortion. The circuit will prevent louder parts of the music composition piece from exceeding the dynamic range allowed within the spectrum. It will basically adjust the volume in real time, on the fly just ever so slightly preventing the loudest parts of the music from clipping or distorting. This helps a great deal but will never get you to at or near the same loudness of a processional FM broadcast radio station.