Why does rasterio compression reduces image size with single band but not with multiple bands

Question

I downloaded Sentinel-2 data. This data have 13 files one for each band as jp2 format. I am reading this images the writing them as GeoTIFF format on python using rasterio. These images are large so I am applying lossless compression to them. I tried both 'deflate' and 'lzw'. I noticed that when I write a single band the image size reduces significantly (the compressed image is 40% the original image). However, when I write a multiple band image, the image does not reduce and in some cases it increases. Can anyone tell me why is that. Below is how I write the images compressed.

new_dataset11= rio.open(
                      'image_multiband_2A/new_multi11.tif',
                      'w',
                      driver='GTiff',
                      width=band_width,
                      height=band_height,
                      count=len(R10m),
                      crs=band_current.crs,
                      transform=band_current.transform,
                      dtype=band_np.dtype,
                      nodata=0,
                      blockxsize=block_size_width,
                      blockysize=block_size_height,
                      tiled=True,
                      compress='lzw')

Answer 1

I think the reason is that rasterio can be problematic when working with multiband images. Maybe for this reason the official documentation only describes the compression of a single band image.

So I would recommend to compress the images afterwards with gdal_translate -of GTiff -co COMPRESS=LZW -co BIGTIFF=YES input.tif output.tif.