Just a quick stab but trying to keep the expense of filming to a minimum.

The radio adaptation of ANH had a nice scene where the Tantive IV faked damage to buy time to receive a transmission from the Rebel spies.

I imagine this must have been an early concept for the film as the scene is as similar to R2's repair to Padme's ship in TPM as the Skyhopper race is to the Podrace in the same film and Lucas loves to recycle unused material.

Another touchstone could be the human mercenaries transmitting the Genesis plans to the Bird Of Prey in Star Trek III.

So what you could have is a small ship seemingly adrift near Bothawui (which is under Imperial blockade) and the human (to avoid makeup effects) Captain is keeping up a story that his ship has broken down and is under repair while in the background he is receiving a transmission from the planet.

The Imperials want to board the ship anyway.

They soon twig on about the transmission but they can't jam it so they start shooting both the ship and bombard the source of transmission (creating obvious damage to the populated area of the planet below).

The transmission is completed however and the ship immediately jumps to Hyperspace.

A spot reading of the transmission mystifies the Captain as it seems to obsolete news (It shows the Death Star which was destroyed in the first film).

But zooming into a small grey shape in the footage we see the other Death Star also being built and the dwell on the horrified look on the Captain's face.