A method for controlling a driving distance between a host vehicle and a first vehicle driving in front of said host vehicle, said host vehicle driving at a driving speed and at said driving distance to said first vehicle, said host vehicle comprising: a system for controlling said driving distance, which is adapted to retain said driving distance at not less than a minimum safety distance, and a fuel saving system, which includes an automatic speed increasing function, which automatic speed increasing function, upon fulfilment of a set of conditions, is activated to automatically increase the driving speed in order to utilise the kinetic energy inherent in said host vehicle to save fuel, the method comprising the steps of: - retrieving information to prepare for activation of said automatic speed increasing function, - preparing for said activation by --setting the minimum safety distance to a first distance, whereby, when said driving distance is less than said first distance, said system for controlling the driving distance will adapt said driving speed until said first safety distance is reached, -- allowing activation of the automatic speed increasing function only when the driving distance is at least said first distance, and upon retrieval of information that said set of conditions is fulfilled, characterised in that - upon activation of said automatic speed increasing function, setting the minimum safety distance to a second distance, said second distance being shorter than said first distance, - such that the difference between the second and the first distances is available during the activity of the speed increasing function to perform an automatic speed increase without conflict with the system for controlling a driving distance. a system for controlling said driving distance, which is adapted to retain said driving distance at not less than a minimum safety distance, and a fuel saving system, which includes an automatic speed increasing function, which automatic speed increasing function, upon fulfilment of a set of conditions, is activated to automatically increase the driving speed in order to utilise the kinetic energy inherent in said host vehicle to save fuel, the method comprising the steps of: - retrieving information to prepare for activation of said automatic speed increasing function, - preparing for said activation by --setting the minimum safety distance to a first distance, whereby, when said driving distance is less than said first distance, said system for controlling the driving distance will adapt said driving speed until said first safety distance is reached, -- allowing activation of the automatic speed increasing function only when the driving distance is at least said first distance, and upon retrieval of information that said set of conditions is fulfilled, characterised in that - upon activation of said automatic speed increasing function, setting the minimum safety distance to a second distance, said second distance being shorter than said first distance, - such that the difference between the second and the first distances is available during the activity of the speed increasing function to perform an automatic speed increase without conflict with the system for controlling a driving distance. - retrieving information to prepare for activation of said automatic speed increasing function, - preparing for said activation by --setting the minimum safety distance to a first distance, whereby, when said driving distance is less than said first distance, said system for controlling the driving distance will adapt said driving speed until said first safety distance is reached, -- allowing activation of the automatic speed increasing function only when the driving distance is at least said first distance, and upon retrieval of information that said set of conditions is fulfilled, characterised in that --setting the minimum safety distance to a first distance, whereby, when said driving distance is less than said first distance, said system for controlling the driving distance will adapt said driving speed until said first safety distance is reached, -- allowing activation of the automatic speed increasing function only when the driving distance is at least said first distance, and upon retrieval of information that said set of conditions is fulfilled, characterised in that - upon activation of said automatic speed increasing function, setting the minimum safety distance to a second distance, said second distance being shorter than said first distance, - such that the difference between the second and the first distances is available during the activity of the speed increasing function to perform an automatic speed increase without conflict with the system for controlling a driving distance.