Fiber-fed spectrographs can now have throughputs equivalent to slit spectrographs. However, the sky subtraction accuracy that can be reached on such instruments has often been pinpointed as one of their major issues, in relation to difficulties in scattered light and flat-field corrections or throughput losses associated with fibers. Using technical time observations with FLAMES-GIRAFFE, two observing techniques, namely dual staring and cross beam switching modes, were tested and the resulting sky subtraction accuracy reached in both cases was quantified. Results indicate that an accuracy of 0.6% on the sky subtraction can be reached, provided that the cross beam switching mode is used. This is very encouraging regarding the detection of very faint sources with future fiber-fed spectrographs such as VLT/MOONS or E-ELT/MOSAIC.