I used old Atahualpa theme and if widged did not have title, it sticked it with upper widget without spacing which is exaclty what I wanted.

In new theme, even if title is empty, space for it is preserved, making uneccessary spacing between widgets.

By looking int theme CSS I found out that now widget outer spacing is set for whole widget (as spacing on bottom), thus, spacing is always there.

I made half-solution by removing bottom spacing for widget and adding top spacing for title. Title shows only if it is not empty, so spacing is there only if title is displayed.

The only problem is that top widget now has extra top spacing which makes things a bit ugly.

You can remove the top padding of the sidebars

td#left, td#right {
padding-top: 0;
}

Sure, but then I loose padding between widgets too. I just want to remove top padding for top widgets.

I can do that (I am pretty fluent in HTML and CSS), just pointing this out because I think it should be solved within original theme code.