Context. The Kepler space telescope has provided time series of red giants of such unprecedented quality that a detailed asteroseismic analysis becomes possible. For a limited set of about a dozen red giants, the observed oscillation frequencies obtained by peak-bagging together with the most recent pulsation codes allowed us to reliably determine the core/envelope rotation ratio. The results so far show that the current models are unable to reproduce the rotation ratios, predicting higher values than what is observed and thus indicating that an efficient angular momentum transport mechanism should be at work. Here we provide an asteroseismic analysis of a sample of 13 low-luminosity low-mass red giant stars observed by Kepler during its first nominal mission. These targets form a subsample of the 19 red giants studied previously, which not only have a large number of extracted oscillation frequencies, but also unambiguous mode identifications. Aims: We aim to extend the sample of red giants for which internal rotation ratios obtained by theoretical modeling of peak-bagged frequencies are available. We also derive the rotation ratios using different methods, and compare the results of these methods with each other. Methods: We built seismic models using a grid search combined with a Nelder-Mead simplex algorithm and obtained rotation averages employing Bayesian inference and inversion methods. We compared these averages with those obtained using a previously developed model-independent method. Results: We find that the cores of the red giants in this sample are rotating 5 to 10 times faster than their envelopes, which is consistent with earlier results. The rotation rates computed from the different methods show good agreement for some targets, while some discrepancies exist for others.