I compressed an GeoTIFF image with both gdal_translate and Global Mapper with LZW compression. The one Global Mapper compressed is much smaller, is almost 30% of the one gdal_translate compressed.
gdal_translate -co COMPRESS=LZW -co TILED=YES -co PREDICTOR=2 1.tif lzw1.tif
How can I compress it further like Global Mapper?