Saving a raster file without including no-data values in Python

Question

I have a file in TIF-format that I am trying to save with rioxarray in Python, but when I save it normally, the file size and height/width is much larger than they should be. If I look at the file with

rds.count

I can see that a lot of the pixels in the image are

array([[[-9999., -9999., -9999., ..., -9999., -9999., -9999.],
    [-9999., -9999., -9999., ..., -9999., -9999., -9999.],
    [-9999., -9999., -9999., ..., -9999., -9999., -9999.],
    ...,
    [-9999., -9999., -9999., ..., -9999., -9999., -9999.],
    [-9999., -9999., -9999., ..., -9999., -9999., -9999.],
    [-9999., -9999., -9999., ..., -9999., -9999., -9999.]]],
      dtype=float32)

Meaning a lot of the data is simply pixels with no value. I was wondering if it is possible to save the file without these pixels to save on storage. I save the file with the following code:

with rasterio.open("new_image.tif", "w", **out_meta) as dest:
    dest.write(out_image)

Where the image is found in the variable 'out_image'. Is there anything to add here to make sure the no-data values are not included? Thanks for any help!