1. A heart stimulator comprising: a. a stimulation pulse generator connected or connectable to at least one stimulation electrode for delivering stimulation pulses to cardiac tissue of a heart chamber, the stimulation pulse generator being adapted to generate stimulation pulses of adjustable stimulation pulse strength, b. a sensing stage for sensing a heart parameter indicative of a contraction of a stimulated heart chamber, c. a capture detector being connected to the sensing stage and being adapted to: (1) evaluate a sensed heart parameter, (2) determine whether a stimulation pulse was captured by the stimulated cardiac tissue of the heart chamber or not, and (3) provide an output signal, the output signal being either: (a) a capture signal if analysis of the sensed heart parameter indicates a contraction of the heart chamber following a stimulation pulse of specific stimulation pulse strength, or (b) a non-capture signal if analysis of the sensed heart parameter indicates no contraction of the heart chamber following a stimulation pulse of specific pulse strength, d. a control unit being connected to the stimulation pulse generator and to the capture detector, the control unit: (1) comprising means for automatic threshold adaptation, the means for automatic threshold adaptation being configured to perform an automatic iterative threshold search wherein: (a) the lowest stimulation pulse strength leading to a capture signal is determined by stepwise increasing or decreasing the adjusted pulse strength in response to a non-capture signal, and (b) the automatic iterative threshold search is performed by use of a Fibonacci search algorithm, (2) wherein the control unit is configured to control the stimulation pulse generator by adjusting the pulse strength according to a pulse strength value to be applied, the pulse strength value to be applied being determined by the means for automatic threshold adaptation.