 <p>You can pass in a function to compute the Jacobian as the <code>Dfun</code> argument to the <code>Minimizer.leastsq</code> method: <a href="http://lmfit.github.io/lmfit-py/fitting.html#leastsq" rel="nofollow">http://lmfit.github.io/lmfit-py/fitting.html#leastsq</a></p> <p>By default the function passed in for <code>Dfun</code> should return an array with the same number of rows as parameters, and each row the derivative with respect to each parameter being fitted. Make sure to specify the parameters with a <a href="http://cars9.uchicago.edu/software/python/lmfit/parameters.html#the-parameters-class" rel="nofollow">Parameters</a> object so that the parameters are treated in the correct order. I believe this this necessary IIRC though it might not matter.</p>