Customize the order of the header contents

Hi,

I would like to change the order of the header contents. Default order is:
1/ Header widget
2/ Site title and tagline
3/ Site logo

I would like to achieve this order:
1/ Site logo
2/ Site title and tagline
3/ Header widget

I have thought following snippet would do, but it did not:

function generate_header_items() 
{
	// Site logo
	generate_construct_logo();

	// Site title and tagline
	generate_construct_site_title();

  // Header widget
	generate_construct_header_widget();
}

What am I doing wrong, please?