editing - Remove a node in QGIS

I want to remove some nodes from a shapefile using QGIS 2.10.1

1. I enable editing


2. I click on the Node Tool


3. I click on a node I want to select (it turns blue)

However, once I select this node I am unable to delete it.

The Delete Selected button is grayed out, as is cut, and pressing delete on my keyboard does nothing.

I assume I am missing something very basic but I can't figure out what it is.