Honeycomb Archive Digital Aset Management demonstrates how to compress jpeg files in the following article.
Jpeg compression is a commonly used method for saving digital images. This produces better results when used on images with variations of tone or color, rather than a line drawing or any other textured graphic. Remember that the lower the quality and size, the more distorted the digital image will be.
Compressing a JPEG image
In this example, we are going to show the different compressions on a gradient image. Click on Save As.

Save the file as a jpg and then click the Save button.

This is where you will be able to choose the jpeg options. From the pull-down menu choose the quality you want to save the jpeg as. You can also use the bar below the pull-down menu to choose the quality of the jpeg. When done click OK.

Here is the digital image saved as the lowest quality jpeg. You can see that the gradient is much harsher and not a smooth transition from the shades.

Here is the same digital image saved as a maximum quality jpeg. Notice the smoothness of the gradient.
