We present high resolution 3-D simulations of the planet-disc interaction using smoothed particle hydrodynamics , to investigate the possibility of driving eccentricity growth by this mechanism . For models with a given disc viscosity ( \alpha = 0.01 ) , we find that for small planet masses ( a few Jupiter masses ) and canonical surface densities , no significant eccentricity growth is seen over the duration of our simulations . This contrasts with the limiting case of large planet mass ( over twenty Jupiter masses ) and extremely high surface densities , where we find eccentricity growth in agreement with previously published results . We identify the cause of this as being a threshold surface density for a given planet mass below which eccentricity growth can not be excited by this method . Further , the radial profile of the disc surface density is found to have a stronger effect on eccentricity growth than previously acknowledged , implying that care must be taken when contrasting results from different disc models . We discuss the implication of this result for real planets embedded in gaseous discs , and suggest that the disc-planet interaction does not contribute significantly to observed exoplanet eccentricities .