lsqcurvefit finds multiple solutions

Does anyone have experience with using lsqcurvefit for fitting set of data? What I want to do is fit my set of data to a function which contains lorentzians. Each set differs from the other very little. I fit every set individually and it works perfectly. What I want to do is take the average value of each parameter acquired that way. Since my data varies very little, the mean value should be very similar to every individual value of each parameter and the average value of parameters should give me the right fit for all data. The problem is that there is more than one solution to lsqcurvefit. When I plot each parameter for the whole data set individually, I see that they are concentrated around two values. What I did was give lsqcurvefit boundaries for every parameter. It works, but is there any other more elegant solution fot this?