In some pre-Crisis retellings, Jor-El wanted to save both Lara and Kal-El by sending them away in the same rocket, but she would refuse saying that the rocket was too small and might not make it to Earth because of her added weight, and she wanted to stay with her husband (an idea that was briefly touched on in Superman: The Animated Series). Byrne's original idea was to show a pregnant Lara leaving Krypton. After landing near Smallville, Lara would immediately succumb to a small chunk of kryptonite that was embedded in the ship's hull. This would have been Byrne's way to show early on how deadly kryptonite was. Lara would then have been found by the Kents while she was in labor, induced by the stress from kryptonite poisoning. Before dying, Lara would have told the Kents to look after her son. They would then take young Kal-El, an alien born on Earth, and raise him as their own just as they promised his mother. This was also Byrne's way to emphasize the Kents being chosen caretakers rather than them being a random couple who finds a baby in a rocket (this concept was also, in a way, touched on in Smallville and Last Son of Krypton). The idea was not used because DC wanted Kal-El to be sent to Earth alone, as all the previous incarnations agreed upon.
Superman was originally going to save a landing space-shuttle. But after the Challengerdisaster, the Constitution was changed to "an experimental space-plane".
Recently, Byrne stated that he regretted ever removed Superman's Superboy career. As Superboy, Clark would have been "learning the ropes"/"figuring it out" (partial reason why he'd Ret Gone it in the first place since he needed Superman "up to speed" for his relaunch) before he reached adulthood as Superman.
Another unused Marv Wolfman idea was having Lois Lane and Lex Luthor romantically involved and living together in Luthor's estate in the mountains until Superman came to Metropolis. Lois would then leave Luthor to go after Superman, another reason for Luthor to hate Superman. This idea was scrapped because Byrne did not want Lois as someone who was drawn to power (and he didn't want any mountains shown alongside the city either). Though the actual comics did mention that Lex and Lois had dated a couple times.