z-index and opacity with one image partially on top of another, how can I remove the transparency?

z-index and opacity with one image partially on top of another, how can I
remove the transparency?

I have two images on my site, one is simply an image ( in the HTML file),
while the other is the background of a container (the main part of the
page) (defined in the CSS file as "background-image:url(x)") added to the
HTML file via a tag. The rest of the page has a background of #eeeeee
(slightly darker white).
The z-indexes of the two are set so the image is on top of the background
image, exactly what I want... However, I can see through the image to the
background image. This is because the has opacity:0.4 as a style
attribute. So it makes sense that it shows through to the background, but
is there any way to make the be transparent through to my #eeeeee
background?