I like to think of different tranches of emergency too, and keep different emergency funds in different vehicles for each type of emergency. General cooling off of the market? Hold Series I bonds or some security that's pretty much as good as cash but has a small amount of growth. Sudden unemployment? Cash in a money market account. Natural disaster like an earthquake that may limit your access to financial institutions? Cash stuffed in the mattress. The zombie apocalypse? Ammunition and bottled water.

Have a little bit of your emergency fund in each of these.