A method for determining the recording power of a laser beam so that jitter from a reproduced signal obtained by reproducing data recorded in a data rewritable type optical recording medium can be controlled within an acceptable tolerance even when cross erasing of data occurs. The power of a laser beam is measured for each level of the recording power of the laser beam. Critical parameters are calculated for each level of the recording power of the laser beam. The critical parameters are projected onto a data rewritable type optical recording medium for recording data therein. Direct overwriting required for saturating an influence of cross erasing of data is performed x times in one embodiment to determine a critical parameter. A data recording apparatus storing a critical parameter used for determining the power of a laser beam is associated with ID data for identifying the kind of optical recording medium. A data recording apparatus storing an optimum recording power used for determining the power of a laser beam is also associated with ID data for identifying the kind of optical recording medium.