Beyond the obvious limitations of expressing large amounts of detail with a small number of pixels, I sense that you're seeing jagged edges around irregularly shaped image elements.
Are you saving GIFs? Keep in mind transparency with GIF is all or nothing. Try saving as PNGs instead as PNG-24 allows partial transparency at the edges of your objects. Or pre-craft your objects not to be irregular, and surround them with the colors of the background they'll be overlaying.
If I've mis-characterized the issue, please post more information, such as screenshots, to show just what you're asking about.
One other possibility comes to mind, though I'm not sure without further information that it applies directly:
In the modern era, with ever increasing Internet bandwidth and browsers that can be zoomed smoothly via gestures (e.g., on tablets), you might consider saving your images at a size larger than they need to be, then making them fit with the other page elements via style attributes of the HTML elements. The result is that when people zoom in they can see more detail. I almost didn't post this, because I don't know whether you're designing your HTML at this level, but I thought I'd mention it. I know that when I'm browsing with my iPad if I want to look more closely at something I just zoom in on it briefly. I'm pleasantly surprised when I encounter images that don't break down and get fuzzy.
That's great! I will try it later and tell you how it worked.
You mention a newsletter in your first post. Is this something you are designing and outputting from Photoshop? It sounds like the answer may be yes.
Something like a newsletter should be created in a an application like inDesign or MS Publisher, and saved as a PDF file. That way you get to choose on the quality of the images it contains.
I edit and produce my Camera Club's newsletter, and I would be happy using an image just 1000 pixels wide because I rarely make one image fill a full page. I save it as best quality for printing, and a dozen A4 pages save at about 3.5Mb of beautifully sharp text and images. This issue has 15 pages and is 2.3Mb