Want to supress tooltips of featured images (or modify the tooltip parameters)

I've got a site that uses tons of posts with featured images. Not a problem. My layout is such that the featured images are right aligned (and with my layout, that puts them very near the right margin of the site) and when I hover over them the tooltip pops up and runs off the page to the right.

1: Is there a way to eliminate the tooltip for those images only? This would certainly be my preference, but I don't want to eliminate tooltips on other elements throughout the site.
or
2: Is there a way to modify the tooltip behavior/settings so that it pops-up to the left/above/below my images?

This is the CSS associated with the featured images.. I'm not sure if that helps or not but here it is anyway.

img.wp-post-image {
background: none repeat scroll 0 0 rgba(0, 0, 0, 0);
border: 1px dashed #000000;
display: inline-block;
float: right;
margin: 0 0 5px 5px;
padding: 8px;
position: relative;
top: -5px;
}