The noise is very important. Any kind of white noise is soothing for a baby... noise from water, car or even vacuum cleaner.. I used to generate a noise with:

  sox -n soothingnoise-3mn.wav synth 3:0 pinknoise tremolo 0.5 30 fade q 5 3:0 30

Worked a treat to make my son sleep.

You're using pink noise, right? I wish it would be less common to kind any kind of noise "white noise", as people might instinctively search for / generate actual white noise, dislike it, and abandon the concept. Pink noise is a particular kind of noise that's much nicer to listen to than white noise. I used it from time to time to block my cow-orkers off.

Awesome! You could do an iterative approach with a grid search to find the most-soothing parameter set!