How can I clip multiple geotiff tiles with a shapefile without greatly increasing the

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I'm using gdalwarp to clip a number of geotiffs (tiles of a larger map) to a polygon described by a shapefile (which is about the size of the overall map, i.e. much larger than individual tiles) using:

gdalwarp -of GTiff -cutline shape.shp -crop_to_cutline tile.tif cropped_tile.tif(where tile.tif actually iterates through all the map tiles in the full code)

This works fine, however the resulting tiles (cropped_tile*.tif) now cover the same geographic area as the shapefile, and consequently have much larger file sizes (2.5M -> 64M). Is there any way to clip the areas of the tiles which lie outside the polygon in the shapefile without making each tile cover the same area as the shapefile itself?

Thanks



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