But the Rebellion wasn't their main concern. Indeed, the Rebel victory that roused the Imperial ire in SWIV was a recent one, postdating the construction of the first Death Star. And SWIII shows that the DS construction began long before there was a Rebellion.
The Imperials saw the Death Stars as key pieces in their doctrine of intimidation. They could achieve much more than their true firepower would warrant - they could win battles or entire campaigns without even being present. In the end, they would be a cheaper way of maintaining the Emperor's grip than "true" firepower would. Plus, fighting back at them would be much more difficult than fighting back at conventional occupation forces, on physical as well as psychological level.
I don't think Palpatine was too far off the mark when deciding that this was the way to go.
Timo Saloniemi