You are resampling images in Adobe Fireworks CS3 and have four options to choose from: Bicubic, Bilinear, Soft and Nearest Neighbor. Compare file sizes and output quality of these choices. Here we resample a single image with different options in Fireworks CS3.
First, the term resampling means you are physically changing the number of pixels in your image, which is what we are doing here. Next, here is an 800 x 600 pixel image resized to 600 x 450 using Bicubic resampling.

Next, we see Bilinear resampling. This image is also 600 x 450 pixels, and is smaller in byte size. Detailed byte sizes are shown after the images.

Third, we see Soft resampling, which is the third option in the drop-down item in Fireworks or Photoshop. This image is larger in byte size than the previous.

Finally, we see Nearest Neighbor image resampling, which has the lowest quality and also the smaller byte size. This is not a reasonable option for most sites and images.

Here is the table containing the sizes. This table shows the dimensions, which are the same for the four images, and also the size in bytes after the images are converted to 64 adaptive colors and after maximum lossless PNG optimization is applied.
Bicubic 19.1 KB (19,621 bytes) Bilinear 14.3 KB (14,657 bytes) Soft 17.4 KB (17,898 bytes) Nearest Neighbor 8.83 KB (9,052 bytes)
Here we saw that for the simple screenshot resized from 800 x 600 pixels, to 600 x 450 pixels, Nearest Neighbor resulted in the smallest file size, but had unacceptable quality. Bilinear resampling produced very good results and the file size was substantially smaller than Bicubic and Soft. Therefore, I recommend Bilinear resampling for screenshots in online technical documents.