Modern web design with data tables that don’t stretch

I am working on what you could call an accounting or payroll software. They want to convert it bit by bit to a web app. The original desktop tool has that 1990's look, relatively small windows packed with data.

Now what they want for the new version is to get that slick, responsive modern web look, but at the same time they still want to have a lot of data and controls on the same page.

They recently told me that they would prefer keeping the data table just wide enough for the data to fit. No stretching basically. Many sections of the apps are basically just data visualization with a mix of charts and tables, so that's a big design change. How do I make this work?

Visual example of a typical page, with some controls and data tables:

Tables 1 and 2 could be much smaller in width. Putting them side by side doesn't solve the general case because table 2 may actually not be shown, depending on the computation. In short I don't see how to set my tables to minimum width without having ugly blank space at the right side of my tables.