That's a big tail for a crane.

the beloved origami crane made more accurately.

I've folded Japanese origami cranes since I was a child, but recently I wondered about the triangle in the back. It doesn't look right. Is it suppose to be a tail? From what I can tell, cranes have relatively short tail feathers. When in flight, the back part should be legs, which are in line with the body.  

Call me crazy, but I propose folding cranes with a slightly altered shape.  It just seems more accurate. 

 Whooping Crane in flight in Texas.  USDA Photo by John Noll

Whooping Crane in flight in Texas.  USDA Photo by John Noll

 There's a new crane in town.

There's a new crane in town.

New cranes spotted in the wild.

If you wish to fold your own paper crane, here are instructions for the traditional crane but it's easy enough to tweek the tail to be legs.  I would love to see which style you choose. Send me a pic on Twitter. My handle is @workshopemei.

 By Origamidesigner - Own work, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=15224121

By Origamidesigner - Own work, CC BY 3.0, https://commons.wikimedia.org/w/index.php?curid=15224121

References: 
Cranes of the World: 2. Individualistic and Social Behavior Paul A. Johnsgard University of Nebraska-Lincoln, Jan 1983