This is how I brew my tea most of the time:
1. Boil water in my stovetop glass kettle (actually a coffeepot, minus the percolator bit, that belonged to my parents - but seeing as they don't use it any more, I nabbed it [politely]).
2. Warm my glass teapot with a bit of the hot water, then pour that water into my green teapot to warm it as well.
3. Put the leaves loose into the glass teapot and pour on the boiled water (after it has cooled a little if necessary).
4. Steep the appropriate amount of time (or longer, if I get distracted... Whoops).
5. Strain the tea from the glass teapot into the green teapot. Drink and enjoy!
So why all the high maintenance and creation of more washing up than is strictly necessary? Well, I can't prove it with science but I really do think that allowing the leaves to float freely produces a better cup of tea... They have the chance to fully open and swirl around. Given that most of my teapots hold more than one cup's worth of tea, though, I need to decant it into a second teapot to prevent oversteeping.
Also, while my glass teapot is good because you can see how pretty the leaves look while they brew, it does have a badly chipped spout and doesn't pour well, making it less than ideal for serving the tea, especially to guests.