How to resize hi-res photos for FB?

[Lauren]

I'm a photographer who is struggling with FB's timeline image compression. Before, I didn't need to resize my images because I never lost any sharpness. Once I started using timeline, these photos were compressed horribly.

I did my research and found in several places that I should be resizing to a width of 960. Even when I do that in photoshop (image -> image size) it still looks terrible, even worse than the compression at he original resolution.

It's looks like an image that has been screencapped several times - it's all pixelated.

Is there a full-proof method of how to do this in photoshop? I'm suffering here... I need to update my page.

Thank you.
Have been doing all that Steve P recommended. Image still uploads looking like crap . . .
I do not wish to crop my images, that would be detracting from the original framing which is an artistic choice.

Not having these images on facebook is not an option. Clients need to be able to use these images.
And I've been selecting the HQ option as well - does nothing.
Wow, that is rather rude of you. Facebook is not the only website I use to host my photos. However it's pretty common sense that clients would like to be able to use these photos for their facebooks. You are no longer helping. I didn't ask about any other websites. Kindly fuck off unless you can actually contribute to my original question which does not include the use of other websites.