A converter for driving a load has a main switch for controlling, at a switching frequency, the path of current flow through a power inductor and power commutation thereof so as to provide an output. A hysteretic control circuit generates a burst signal for turning on and off the power commutation to implement a burst mode operation with a burst frequency lower than the switching frequency. An adjusting circuit adjusts the upper threshold and/or the lower threshold of the hysteretic control in dependence on the detected burst signal. This burst mode hysteresis controlled converter in this way has the hysteresis adapted in dependence on the load being driven so that load regulation problems are reduced.