I'd tell you to just buy Svedka if you want something cheap but quality. Haven't had it in years but I know we had at least one long cabin weekend and that was the drink of choice - pretty smooth and no headaches.

I have heard of people putting cheap vodkas through a carbon filter (like Brita) a few times to improve smoothness. I haven't tried it myself, but I am skeptical, because if the fix is that easy then it seems like the producer would have done it. MythBusters did a double-blind taste test[0] in which only the "vodka expert" was able to correctly rank the samples, and they found that the chemical composition of the cheap vodka was the same before and after filtering. Based on that, I would say the answer is most likely "no" and you should spend a few more bucks.

[0]: http://kwc.org/mythbusters/2006/04/episode_50_bullets_fired_...

Yes & no. While you could redistill it and be extra generous with the amount of head (& tail?) thrown away. Or you could build a activated carbon filter; if you search around there is a lengthy PDF describing the proper dimensions & volume of carbon filtration needed. The cost of the activated carbon is probably going to exceed just buying slightly more expensive such as Costco/Kirkland vodka. It's not as cheap as the plastic bottle brands like Taaka but save for really high consumption levels it's probably cheap enough.

I know a guy in Aarhus, Denmark once that was triple distilling floor cleaner. He still had his vision and all organs intact, but I still did decline the offer of a drink at his house...

it's not really about holding it at a proper temperature, it's where things boil and evaporate. if you redistill a vodka, you can typically remove more impurities.

I've done double blind vodka tastings and some of the cheaper vodkas come out on top. e.g. Barton's is as good as top-shelf (that were in the tasting)