I hate to be the bearer of bad news... but there isn't really much of a difference between 但是 and 可是 in everyday speech. Both have the same meaning, and the two are almost interchangeable.
I know, back in school, we learned about the basic sentence constructs, "虽然...但是..." being one of them (along with the well-known "一边...一边...", among others), but that is school. In everyday conversations, how many of us actually start a sentence with "虽然" just so that we can use the "但是" ? Most of the times, the "虽然" is simply dropped. For simplicity's sake, sometimes, certain parts can be, and are omitted/neglected/abbreviated in Chinese. In fact, Chinese tend to use "但是" more so than they would use "虽然...但是...", "可是", "不过" or "但...". But the others are there to add variances to your sentences. That isn't necessarily a bad thing.
The only thing that I'll like to point out is that "虽然...但是..." is the more complete expression, and it has a more formal feel to it.
ps: Natives, no matter the language, they have their own habit of saying certain things. For people who are non-native to that language, we'll just have to adapt.