I know a little bit.

On this side of the pond, laser lithotripsy is seen as a promising nonsurgical treatment of bile stones, which can work in cases where shockwave lithotripsy doesn't work or is unsuitable for the patient, but it is still in clinical trials.
Personally, I'd be very reluctant to have it done unless I knew the person had been properly trained, because of the danger of lasers causing tissue damage in inexperienced hands.
Is the stone, or you, unsuitable for shockwave lithotripsy, or basket removal?