Wordpress text wrap around image

I'm trying to do something that I thought would take 2 minutes and instead has taken up 2 hours... When you insert an image into Wordpress, it automatically puts it into a paragraph. I'm trying to get subsequent paragraphs to wrap around the image, and nothing's working for me. My CSS is:

p img.alignleft {
    float: left;
}

p {
    float:left;
    clear: none;
}

What the heck am I missing?!