Theoretical models predict that fast-flowing ice streams transmit information about their bedrock topography most efficiently to the surface for two distinct windows of length-scales. Previous studies have shown a good transfer for basal undulations with wavelengths longer than 103 ice thicknesses. In addition, a local maximum in the theoretical transfer function appears for intermediate wavelengths between 1 and 20 ice thicknesses. So far, however, no experimental evidence for this important transfer at intermediate wavelengths has been obtained. In our work we use recently acquired radar data for the Rutford Ice Stream and Evans Ice Stream to provide the first experimental confirmation for this theoretical prediction, and show that fast-flowing ice is highly transparent to bedrock irregularities with wavelengths between 1 and 20 ice thicknesses. The amplitude of this local maximum depends on various flow parameters such as Glen's flow law exponent and the slip ratio, i.e., the ratio between mean basal sliding velocity and mean deformational velocity. We find that higher values of the slip ratio generally lead to a more efficient transfer. Our results underline the importance of bedrock topography for ice stream dynamics, and exclude basal slipperiness as the only determining factor for variations in the flow regime and surface topography. In the second part of this work, we address the role of the basal sliding law in statistical inversion methods that use surface data (topography and velocity) to obtain information about the basal slipperiness distribution and bed topography. We show that different sliding laws generally lead to the retrieval of different but equally realistic basal conditions. Since the correct form of the sliding law is still disputed, the use of inversion methods to obtain unambiguous information about the bed therefore remains problematic.