A high quality texture filtering technique in a computer hardware system. The texture filtering quality of the present invention is comparable to trilinear filtering. However, the present invention reduces the number of memory accesses by fifty percent in comparison to trilinear filtering. To achieve this result, the present invention determines a pixel value based upon one or more texel values, e.g., four texel values, from only one of two mipmap levels. The mipmap level that is used is based upon the fractional portion of the LOD value and the position of the pixel. For a group of pixels having the same LOD value, the present invention performs a dithering operation that results in some pixel values being determined using texel values from the lower level mipmap and the remaining pixel values being determined using texel values from the higher level mipmap. The percentage of pixel values that are determined using texel values from the higher level mipmap is proportional to the fractional portion of the LOD value.