Photoshop :: Adding Jpeg Artefacts To Image On A...

I have a low resolution image 'A' from someone that has been jpg'd, perhaps a few times. It has pixels that are visible without too much effort, and edges to objects that are not regularly stepped, say 3px wide then 1px down in places (lets call this vari-stepped). Studying the image, the pixels are in fact formed into blocks or squares of pixels.

I now have taken into this image part of another far better image 'B' and need to make it look like it belongs there. Adjusting colours and focus and softening edges is one thing, but it needs that jpg artefacting adding. Simply dealing with the addition beforehand and lowering its resolution doesnt do it, as the resulting pixels are not blocky, edges are not vari-stepped. The jpg feel to it is not there.

What controls can I use to achieve this on the image in that layer after its brought in, with Photoshop CS2 or even P'shop 7 which I still use as I prefer layer links there ! By working in the image I can compare effects to the recipient image. Perhaps only the latest Pshop has what I need ?

Pixelate filter is not enough, its too crude, lowest setting is too much, it doesnt do the blocky look, or the vari-steps.

Getting a better image 'A' is not an option.

It would be great to have an ability to tell P'shop to analyse the image 'A' and apply settings to make image 'B' the same.