I would like to use web.config to redirect all requests on my asp.net site to https:// with non-www. That is:
http://
http://www
https://www
You need to add second rule:
<rule name="NonWwwRedirect"  stopProcessing="true"> 
    <match url="(.*)" /> 
    <conditions> 
        <add input="{HTTP_HOST}" pattern="^www.sitename\.com$" /> 
    </conditions> 
    <action type="Redirect" url="http://sitename.com/{R:1}" /> 
</rule> 
You just need to replace sitename.com with your domain name