We present the results of the first joint search for gravitational-wave bursts by the LIGO and GEO 600 detectors. We search for bursts with characteristic central frequencies in the band 768 2048 Hz in the data acquired between 22 February and 23 March, 2005 (fourth LSC Science Run S4). We discuss the inclusion of the GEO 600 data in the Waveburst CorrPower pipeline that first searches for coincident excess power events without taking into account differences in the antenna responses or strain sensitivities of the various detectors. We compare the performance of this pipeline to that of the coherent Waveburst pipeline based on the maximum likelihood statistic. This likelihood statistic is derived from a coherent sum of the detector data streams that takes into account the antenna patterns and sensitivities of the different detectors in the network. We find that the coherent Waveburst pipeline is sensitive to signals of amplitude 30 50% smaller than the Waveburst CorrPower pipeline. We perform a search for gravitational-wave bursts using both pipelines and find no detection candidates in the S4 data set when all four instruments were operating stably.