Hi Bill - it's possible to do that by removing the object's name and setting it to blank.

Select the objects that you want to have removed, then click on the name line in the properties panel here:



The "Edit object name" dialog box will pop up - push delete to remove the text and push OK or press Enter and that will erase the name on those objects and they will no longer belong to that slot in the Objects section of the scene browser.

- Michael