Keeping a database connection with a Singleton?

[exhuma.twn]

I remember reading about the Singleton pattern in python and how it's
an unpythonic pattern and all. At the time I did not need the
Singleton anyways, so I just glanced over the document.

But, setting this aside: I have an application where I have a
connection to a database. At some point in the application I open up a
new window. The new windows resides in a different module. So I have a
directory structure like this:

- mainapp.py
- newwindow.py

So I import "newwindow" in "mainapp"  so I can instantiate and display
it. Meanwhile, the main-app has an open connection to the database.
What's the cleanest way to hand this connection to the new window? I
can see several possibilities:

1) Simply pass the connection as paramtere to the constructor of new-
window.
2) Use the "Singleton" deisign pattern to keep a reference to the
connection
3) Open up a completely new connection to the database in the new
window.

Now, option 1) is clearly the easiest to implement, however, I somehow
tend to use option 2 (the singleton) as it's more flexible. Option 3
looks ugly to me.

This is a stuation I run into many times. And I am always faced with
the same choice. And I never know which one to chose. And now that I
am getting more and more comfortable with the basics of python, I
would like to know if I am missing something more "pythonic".

So, what would you recommend?