JPG compression is most appropriate for images that employ millions of colours and fine colour gradients, such as photographs or background gradients.
JPEG (JPG) compression is complex, but it's easy to learn and understand the basics. Find out how JPG compression works, mathematically and algorithmically. You'll develop a good sense of what its strengths and weaknesses are, and you'll be able to choose the right compression method for your images.
The one built in to PhotoShop/Imageready is pretty good, but it doesn't offer extreme compression the way a third-party specialized compressor does.
It isn't well known that JPG compression allows some areas of your image to be highly compressed, while other areas may be shown with crisp detail. A good JPG compressor will let you choose different compression levels for areas of the image, thus letting you drastically reduce file size without compromising image clarity.