We present a comparison between our strategy of computing new adiabatic pulses and the best results given so far in the literature by Rosenfeld and co-workers. Our technique has been described elsewhere and is based upon a simple physical idea (the adiabatic factor is offset-independent) and an evolution strategy algorithm which stochastically searches for a `solution' with optimal inversion profile and power characteristics. As expected for all adiabatic pulses, the inversion profiles are similar for our solutions and those of the literature. On the other hand, some of our pulses offer a substantial reduction of peak and average power relative to the solutions of Rosenfeld. We discuss the properties of the families of analytical functions, where, in our opinion, it is convenient to search for a pulse shape with optimal inversion profile and power characteristics.