Aberrating materials can degrade acoustic measurements by distorting the acoustic wavefront and causing acoustic speckle (as opposed to speckle noise which is a manifestation of coherent backscatter). The amplitude and phase fluctuations associated with acoustic speckle can introduce considerable measurement uncertainty which is difficult to deal with. This paper demonstrates a new technique which optimises the spatial distribution of the generation of the ultrasound to compensate for the aberration. This technique uses experimentally measured Green's functions to allow the calculation of the field resulting from the generation wavefront during optimisation. The technique is used to improve the accuracy of velocity measurements in a steel sample using 82 MHz SAW waves. This is achieved by optimising for improved spatial coherence in the measurement region which suppresses the speckle noise. Experimental evidence of acoustic aberration arising from grain structure is shown for steel and aluminium and the measured Green's function optimisation technique is shown to overcome the resulting acoustic speckle. The technique was performed using the Adaptive Optical Scanning Acoustic Microscope (AOSAM) at Nottingham University, UK.