Seafloor compliance is the measure of seafloor deformation under a pressure signal. Our new 2-D finite-difference compliance modelling algorithm presents several advantages over the existing compliance models, including the ability to handle any gridded subsurface structure with no limitations on the gradients of the material properties, as well as significantly improved performance. Applying this method to some of the problems inaccessible to previously existing methods, demonstrates that lateral variations in subsurface structure must be accounted for to adequately interpret compliance data. In areas with significant lateral variations, the utilization of 1-D modelling and inversion is likely to result in high interpretation errors, even when additional subsurface structure information is available. We find that flattened pure melt bodies have a significantly higher compliance than cylindrical melt bodies with the same cross-sectional area. The compliance created by such bodies often has side peaks over their edges, which are as strong as or stronger than the central peak, requiring a series of measurements to best constrain their size and shear velocity. Finally, we find that the compliance data are far and away most sensitive to the broad, thick, lower-crustal partial melt zone. Our simple data fitting model for the compliance measurements on the East Pacific Rise at 9 degrees 48'N required shear velocities as low as 700 m s(-1) in the centre of this zone, far below the values previously estimated using 1-D model based inversions, suggesting higher melt percentages than those previously estimated, while small melt bodies in the upper part of the crust were found to have little or no effect on the measured compliance.