A number of optical communication and switching systems, such as those employing frequency division multiplexing (FDM) and frequency modulation (FM), requires lasers capable of frequency tuning, as well as high-speed frequency modulation and switching. Multisegment distributed feedback (DFB) diode lasers can satisfy simultaneously the above requirements. In this paper, we extend our analysis of high-speed frequency modulation in DFB lasers with two active segments. The strong FM response in such lasers is very different, in both magnitude and phase, for the red- and blue-shifted static tuning regimes. We introduce the frequency step-response function to characterize in time domain the dynamics of laser frequency switching from one value to another. This time domain picture shows clearly the effects of magnitude and phase variation of the FM response on the switching behavior of the laser. We define the frequency switching speed of the laser and observe a tradeoff relation between this speed and the magnitude of the FM response, as characterized by the magnitude-speed product. Our results indicate that with optimum laser parameters and operating conditions, the frequency switching rate, and thus also the frequency shift keying (FSK) modulation rate, can be extended to the multigigahertz range (> 8 GHz).