Reducing conflicts between drivers and assistance systems has become an important issue in recent times, resulting in a need for a better understanding of how humans drive. Current models of driver speed choice on curved roads do not model accelerator and brake pedal deflections, and consequently do not account for the fact that deceleration usually occurs in two distinct phases. The contribution of this work lies in the combination of studies of driver’s visual fixations during curve driving with research on how drivers use time thresholds as safety margins, resulting in a more realistic computational driver model that uses thresholds on a single visual perceptual variable to trigger the release of the accelerator and the application of the brakes. A simulator experiment showed that, after individualization of the thresholds using a binary classification method, the model is capable of accurately capturing the speed adaptation of 15 human drivers on single lane roads with multiple curves.