Who but a discerning photographer bothers about artifacts Manfred
And I did more than adjust compression but also down-sized.
I follow your description of the Photoshop process but with PSP I adjust on a 1-100 scale to get the Kb read-out I need for the site .. though as I mentioned now with broadband I'm lazy and do not bother about compression except for one site which requires no more than 100Kb or it doesn't show with the text but as a link.
Actually I may know and dislike them but I am not sure what an artifact is that so many get in a twist over. Another heretical pronouncement