[css] adding css class to multiple elements

I have created a CSS class called 'button' and applied it to all of my INPUT tags by simply using :

.button input
{
//css stuff here
}

<p class="button">
<input type="submit" Name='submit' value="Confirm Selection"/>
</p>

which works fine, but I then added another button, but this isn't part of my form, it is just a place holder which is trigerred with javascript, and opens an iFrame. As I wanted it to look the same as all the 'real' buttons I used the same class.

<p class="button" id="AddCustomer">
<a href="AddCustomer.php">Add Customer</a>
</p>

The Problem I had was that if I left the class as .button input the <a> tag didn't see it. If I removed the input part of the CSS all my buttons got grey squares in the middle.

So I resolved it with .button input,a

This worked fine. . . Until I looked at another page, and found all of my <a> tags were now formatted with the 'button' class, even though they don't have this class applied.

My question then is how can I apply the same CSS class to <input> and <a> tags at the same time, but only if I have explicitly added class="button".