This would be a short post, but I've realized that some people don't know how a dryer or a dehumidifier actually work. So, real quick – a dryer passes air over wet clothes, the moisture evaporates and is carried away by the air, warmer air can hold more moisture, so a hotter dryer setting will dry things faster. A dehumidifier passes air over a cooled coil where the water will condense (like on the side of a drinking glass) and is then pumped away.
Here's what bugs me about clothes dryers – they heat up the air, remove some moisture from the clothes, and then pump that air out of the house. It seems a lot like turning on your furnace and then opening up all the doors and windows in your house, it just wastes energy. Also, since the pressure in a house will always try to equalize itself with the outdoors, outside air will sneak in (through window/door cracks) at the same rate as the air being pumped out by the dryer.
My idea is to put a dehumidifying unit inside a dryer. This way air can be heated up and recirculated within the dryer. The only thing that will leave the dryer will be the condensing water, which would be pumped to a drain. This idea would only work with electric dryers though, since a gas dryer has to vent the fumes out of the house, otherwise bad things happen to you.
I'm not sure of the efficiency of dehumidifiers, or the cost to run them, but if people leave them running in basements it can't be too horrible. Plus, it seems like it'd be very hard to be less efficient than heating up a bunch of air and then pumping all of that heat outside. This dryer/dehumidifier setup would also probably be a lot more efficient than your standard basement dehumidifier for two reasons – 1) it's a small enclosed area and 2) the air it's removing the humidity from has been heated up and has more water to pull out of it than normal room temperature air.
Someone build one of these, and make it affordable. I'm thinking of making a small unit that can be retrofitted onto an existing (electric) dryer.
And while we're on the topic of efficient clothes drying.. I've just started running the dryer less, and then hanging the slightly damp clothes to finish air drying. If I'm going to be using an inefficient beast of a machine to dry my clothes, I might as well use it less. (The clothes from my last couple of batches that I dried like this are also less wrinkly.)