It's hard to answer the question of whether we should limit the use of drones to active, armed conflicts without invoking Humpty Dumpty. In Lewis Carroll'sThrough The Looking Glass, Alice challenges Humpty Dumpty's definition of the word "glory." The ensuing exchange has long been beloved by both linguists and lawyers:
"When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean -- neither more nor less."
"The question is," said Alice, "whether you can make words mean so many different things."
"The question is," said Humpty Dumpty, "which is to be master -- that's all."
Humpty Dumpty knew that arguments about the meaning of words have as much to do with power as with dictionaries, and so it is with drone strikes. Would limiting their use to "active, armed conflicts and for known terrorists" make drone strikes "Acceptable"? Well... it depends what you mean by "active, armed conflicts," what you mean by "known," what you mean by "terrorists," and what you mean by "acceptable."
Here's the basic problem. Under international law and U.S. law, there are different rules for armed conflicts than for ordinary, peacetime situations. To put it starkly, in peacetime, you can't just go around killing people. Try it! (No, don't try it, not really). Just consider the likely outcome if you wander outside and bash a passerby over the head with a brick. You know what will happen, right? You'll be arrested and charged with murder. You could try saying to the arresting officer, "But officer, the guy I killed was my enemy," but odds are this will just add a mental health evaluation to your woes.
During an armed conflict, though, the rules are different. If you're a combatant, and you see someone approaching who you believe might be an enemy, you get to shoot first and ask questions later. In wartime, soldiers have what's called "combatant immunity:" they don't get prosecuted as murderers for killing other people, provided that their lethal acts are consistent with general law of war principles (these include the principles of distinction, necessity, and proportionality).
I'm radically oversimplifying, but you get the basic idea: many things that are unlawful in the absence of an active armed conflict are lawful during an armed conflict, and this applies to drone strikes just as it applies to the use of lethal force via grenade, gun, or slingshot.
So, can you lob a grenade -- or fire a Hellfire missile from a Predator drone -- into a building full of sleeping people? Generally yes, if there's an armed conflict, you're a combatant, and you reasonably believe the building is occupied by enemy soldiers. Generally no, if there's no armed conflict. The police, for instance, can't just decide to blow up a house in which suspected felons lie sleeping.
So a great deal hinges on whether or not we classify something as an armed conflict -- and this is where Humpty Dumpty comes in. The war in Afghanistan is clearly an armed conflict -- no one disagrees with that premise. But is the U.S. in an "armed conflict" with militants in Pakistan, or suspected Al-Qaeda associates in Yemen, or members of the Al Shabaab organization in Somalia?