How can I make my columns different sizes using GridLayout in swing?

I'm using a GridLayout and my code is as follows:

int changingVar = 1;

JPanel panel = new JPanel(new GridLayout(changingVar, 2));
panel.add(new JButton("BUTTON1"));
panel.add(new JButton("BUTTON2"));

This looks like:

___________________________________________
| [      BUTTON1     ] [     BUTTON2     ] |
___________________________________________

which is two evenly sized columns. I would like to make it like this:

___________________________________________
| [          BUTTON1         ] [ BUTTON2 ] |
___________________________________________

in which one column takes up more of the panel space then the other. How do I do this with gridlayout? I am not oppose to using another layout as long as I can have a varying amount of rows and columns that are two different sizes.

Thanks