How to build with web player templates?

Hi, I am trying to set up a build using web player templates, but I think I am missing something in the player or build settings. I made a subfolder in my Assets folder named WebPlayerTemplates with a subfolder named SummersDay (name of my project). I then created a text file named index.html and pasted in the example template from Unity docs and put that in the SummersDay folder along with a thumbnail.

In the PlayerSettings tab of the Inspector, I put the name of the product (SummersDay) and company name (bitsong) in the cross-platform settings and chose SummersDay WebPlayer Template thumbnail which did appear.

In the Build Settings I chose Web Player, Streamed, and when the save dialog came up, I chose the SummersDay folder I had made, but the build made a new folder named WebPlayer under SummersDay and put WebPlayer.html and WebPlayer.unity3d files there. Is this correct? I don't think so. The name SummersDay did not appear anywhere, and %UNITY_UNITYOBJECT_DEPENDENCIES% appeared at the top, and there was a "download player" icon even though I have the player installed. What am I doing wrong? Thanks.

Zaffer