I love playing with a small empire. Being successful depends on your opponents however. If one is carving out a huge empire you are gonna have problems. However, if it remains relatively peaceful, you can win with a 6 city empire. I had a game as Darius on Immortal where I had 6 cities, and 2 got culturally pressured beyond belief, one had already flipped early, and I won a space race. I had cottaged up my empire and I had taken the Khmer capital also, so I had two really good spots. As long as your competitors are relatively close on technology, and there is no breakaway AI in that regard, then the Internet almost always guarantees a space race victory. You just have to be clever in your tech choice and space-ship build order.
I'm not sure how successful a small empire can be on deity, I hope to try it out one day, but for now all I can say in confidence is that as long as there is no breakaway AI, a 6 city victory is very possible on any difficulty through Immortal.
Oh you wanted tips let me add... I'm more of a cottage person so I know this strategy works. I usually cottage most cities that I can and save maybe one good production city. The production will be low during the game, so I usually stick in slavery for quite a while and almost never hit caste system. My late game civics are all those bottom liners, minus environmentalism (free market instead). Late game, your towns will give ok production, if you are on a river the levees will be a huge help. If you plan to win late I'd try to settle on rivers as much as you can as levees are a pretty big deal (and fresh water health bonus!). Also, those customs houses and harbors really help the coastal cities, adding the extra trade route with free market is huge here. You definitely want to save a great engineer for Mining Inc, and if you can get Sid Sushi thats great too. Put this in your Wall Street city of course, you will most likely have your slider at 90-100% the entire endgame unless your diplomacy isnt good enough to keep you out of a war, or if one is just inevitable.
If you are going for space, the important thing is to beeline right to Internet. The late game techs you care about are corporation for Wall Street, then the one for Mining Inc (I believe railroad?). After that, go straight to computers. On the path, you will also have a shot at the Three Gorges Dam, its very nice if you get it, but not at all crucial. It only takes two-four turns to build a power plant, and if the health is really killing you then maybe you could switch to environmentalism. However, there is another way, more on this later. Once you get Internet you will probably get things up through rocketry at least. This is of course if there is parity at the top, otherwise it can be a problem. If you are getting blown away by one strong competitor with GNP much higher than yours, then you should have probably made a move to cripple them earlier. So back to the techs, after you get computers, go for robotics. If you are lucky, the Internet will have given you the other technology for the Space Elevator, if not, research it yourself, I'm pretty sure its Satellites. After this, get superconductors to get your laboratories up. Now you are all set. Its perfectly fine if you haven't even began Apollo yet, even if other teams are beginning to build parts. With the Space Elevator and laboratories, you will catch up in no time (hopefully you got aluminum, otherwise found the corporation... granted you have coal... if not, its still very doable so don't panic). Now you can make your decision, if health is now crippling your empire, grab genetics after superconductors. This will give +3 health per city which is a huge help. Otherwise, go straight after fusion and get the engine(s) built. Usually you can easily build both, I don't think I've ever launched in a small empire with just one engine. You will most likely be producing faster than you are teching through the tree, even with a cottaged empire. You only really need two legit production site, and a town/ levee/ US city is perfectly fine for this as the second best production city. Now, just pick up whatever pieces you still need and launch. Also, you would be wise to put a spy and a security bereau in any city building spaceship parts, as they will be targetted.
Is it possible?
