A method for controlling an elevator includes controlling the speed of a vertically moving elevator car during its run from a starting landing to a destination landing according to speed settings, the speed settings defining a constant target speed for the elevator car. The method includes obtaining measurement data of the ongoing run, which measurement data describes vertical speed and/or vertical acceleration of the vertically moving elevator car, determining whether the measurement data meets one or more predetermined criteria indicating unintended vertical speed and/or unintended vertical acceleration, and changing the speed settings of the current run by lowering the constant target speed from a first constant target speed to a second constant target speed if the measurement data meets said one or more predetermined criteria, continuing the run without intermediate stops to said destination landing. An elevator is provided to implement the method.