FIREFLY (Fitting IteRativEly For Likelihood analYsis) derives stellar population properties of stellar systems, whether observed galaxy or star cluster spectra or model spectra from simulations. The code fits combinations of single-burst stellar population models to spectroscopic data following an iterative best-fitting process controlled by the Bayesian Information Criterion without applying priors. Solutions within a statistical cut are retained with their weight, which is arbitrary. No additive or multiplicative polynomia are used to adjust the spectral shape and no regularization is imposed. This fitting freedom allows mapping of the effect of intrinsic spectral energy distribution (SED) degeneracies, such as age, metallicity, dust reddening on stellar population properties, and quantifying the effect of varying input model components on such properties.