Photoshop Elements :: Reducing Image Size Loses Sharpness

I have a background that has 8.5" x 11" external dimensions.  In the project bin, I'm also showing a layer (with transparent edges) that I've resized to 1" x 1.5".  When I double-click the background to put it on the screen, and then drag the layer  onto the screen, why doesn't it look like a small picture on top of a big one?  Instead, it's huge, and I have to drag it down to size with the move tool!
 
And now, the entire story:
 
Running PSE9 under Mac OS X 10.6.8 Snow Leopard.
 
My project is a montage of stamp-sized images on a letter-size background, as in the attached -- commemorating the woman in the centerpiece.  I've stumbled though this kind of effort before with great success.  This time the small photos are coming out blurry, and it's because this time I've done one thing differently.
 
In prior efforts, I recall somehow reducing the outside dimensions of an open file to about 2" x 3" before editing and finally adding it as a layer to the big background (using Move Tool to size it to fit), although during editing I was working with a reasonably-sized image and not a stamp (probably using command +).  The images in the final version were all sharp.   On this effort, however, cannot remember how to do it the same way, and I ended up working with the original photo, and then when I added it as a layer, I reduced it using the move tool -- very clumsy in view of the fact that the edited layer's image seemed to be larger than the canvas I was building, and the final images were blurry.